I've just tried 15.05.1 and it looks like same switching internal switch problem. In this reléase I can get into console:

root@OpenWrt:/# dmesg | grep switch
[    2.340000] switch0: Atheros AR8327 rev. 2 switch registered on mdio-bus
[    8.100000] mount_root: switching to jffs2 overlay
root@OpenWrt:/#

This time I've tried to configure default ssid OpenWrt chaging value disbled from '1' to '0' and router brings up the blue LED of WiFi but I can't see any network broadcasting OpenWrt...

I've seen /etc/config/network file but I can't understand ifaces....

swconfig dev switch0 show the following:
Failed to connect to the switch. Use the "list" command to see which switches are available.

but listing is empty:
root@OpenWrt:/#swconfig list
root@OpenWrt:/#

(nothing...)

Starting kernel ...

[    0.000000] Linux version 3.18.23 (buildbot@builder1) (gcc version 4.8.3 (OpenWrt/Linaro GCC 4.8-2014.04 r47269) ) #1 Sun Jan 31 15:02:30 CET 2016
[    0.000000] SoC Type: Ralink RT3883 ver:1 eco:5
[    0.000000] bootconsole [early0] enabled
[    0.000000] CPU0 revision is: 0001974c (MIPS 74Kc)
[    0.000000] MIPS: machine is TRENDnet TEW-692GR
[    0.000000] Determined physical RAM map:
[    0.000000]  memory: 04000000 @ 00000000 (usable)
[    0.000000] Initrd not found or empty - disabling initrd
[    0.000000] Zone ranges:
[    0.000000]   Normal   [mem 0x00000000-0x03ffffff]
[    0.000000] Movable zone start for each node
[    0.000000] Early memory node ranges
[    0.000000]   node   0: [mem 0x00000000-0x03ffffff]
[    0.000000] Initmem setup node 0 [mem 0x00000000-0x03ffffff]
[    0.000000] Primary instruction cache 64kB, VIPT, 4-way, linesize 32 bytes.
[    0.000000] Primary data cache 32kB, 4-way, PIPT, no aliases, linesize 32 bytes
[    0.000000] Built 1 zonelists in Zone order, mobility grouping on.  Total pages: 16256
[    0.000000] Kernel command line: console=ttyS0,57600 rootfstype=squashfs,jffs2
[    0.000000] PID hash table entries: 256 (order: -2, 1024 bytes)
[    0.000000] Dentry cache hash table entries: 8192 (order: 3, 32768 bytes)
[    0.000000] Inode-cache hash table entries: 4096 (order: 2, 16384 bytes)
[    0.000000] Writing ErrCtl register=00000000
[    0.000000] Readback ErrCtl register=00000000
[    0.000000] Memory: 61236K/65536K available (2632K kernel code, 126K rwdata, 540K rodata, 148K init, 190K bss, 4300K reserved)
[    0.000000] SLUB: HWalign=32, Order=0-3, MinObjects=0, CPUs=1, Nodes=1
[    0.000000] NR_IRQS:256
[    0.000000] CPU Clock: 500MHz
[    0.000000] Calibrating delay loop... 249.44 BogoMIPS (lpj=1247232)
[    0.070000] pid_max: default: 32768 minimum: 301
[    0.070000] Mount-cache hash table entries: 1024 (order: 0, 4096 bytes)
[    0.080000] Mountpoint-cache hash table entries: 1024 (order: 0, 4096 bytes)
[    0.090000] pinctrl core: initialized pinctrl subsystem
[    0.100000] NET: Registered protocol family 16
[    0.110000] rt3883-pci 10140000.pci: mode: PCIe
[    1.710000] PCI host bridge /pci@10140000/host-bridge ranges:
[    1.720000]  MEM 0x0000000020000000..0x000000002fffffff
[    1.730000]   IO 0x0000000010160000..0x000000001016ffff
[    1.750000] rt2880_gpio 10000600.gpio: registering 24 gpios
[    1.760000] rt2880_gpio 10000600.gpio: registering 24 irq handlers
[    1.770000] rt2880_gpio 10000638.gpio: registering 16 gpios
[    1.780000] PCI host bridge to bus 0000:00
[    1.780000] pci_bus 0000:00: root bus resource [mem 0x20000000-0x2fffffff]
[    1.790000] pci_bus 0000:00: root bus resource [io  0xffffffff]
[    1.800000] pci_bus 0000:00: No busn resource found for root bus, will use [bus 00-ff]
[    1.810000] pci 0000:00:01.0: BAR 8: assigned [mem 0x20000000-0x200fffff]
[    1.820000] pci 0000:00:01.0: BAR 1: assigned [mem 0x20100000-0x2010ffff]
[    1.830000] pci 0000:01:00.0: BAR 0: assigned [mem 0x20000000-0x2000ffff]
[    1.840000] pci 0000:00:01.0: PCI bridge to [bus 01]
[    1.840000] pci 0000:00:01.0:   bridge window [mem 0x20000000-0x200fffff]
[    1.850000] pci 0000:00:01.0: of_irq_parse_pci() failed with rc=-22
[    1.860000] Switched to clocksource MIPS
[    1.870000] NET: Registered protocol family 2
[    1.870000] TCP established hash table entries: 1024 (order: 0, 4096 bytes)
[    1.890000] TCP bind hash table entries: 1024 (order: 0, 4096 bytes)
[    1.900000] TCP: Hash tables configured (established 1024 bind 1024)
[    1.910000] TCP: reno registered
[    1.920000] UDP hash table entries: 256 (order: 0, 4096 bytes)
[    1.930000] UDP-Lite hash table entries: 256 (order: 0, 4096 bytes)
[    1.940000] NET: Registered protocol family 1
[    1.950000] rt-timer 10000100.timer: maximum frequency is 10131Hz
[    1.970000] futex hash table entries: 256 (order: -1, 3072 bytes)
[    1.990000] squashfs: version 4.0 (2009/01/31) Phillip Lougher
[    2.000000] jffs2: version 2.2 (NAND) (SUMMARY) (LZMA) (RTIME) (CMODE_PRIORITY) (c) 2001-2006 Red Hat, Inc.
[    2.020000] msgmni has been set to 119
[    2.030000] io scheduler noop registered
[    2.030000] io scheduler deadline registered (default)
[    2.050000] Serial: 8250/16550 driver, 16 ports, IRQ sharing enabled
[    2.060000] console [ttyS0] disabled
[    2.070000] 10000c00.uartlite: ttyS0 at MMIO 0x10000c00 (irq = 20, base_baud = 2500000) is a 16550A
[    2.090000] console [ttyS0] enabled
[    2.090000] console [ttyS0] enabled
[    2.100000] bootconsole [early0] disabled
[    2.100000] bootconsole [early0] disabled
[    2.120000] 1c000000.nor-flash: Found 1 x16 devices at 0x0 in 16-bit bank. Manufacturer ID 0x0000c2 Chip ID 0x0022cb
[    2.140000] Amd/Fujitsu Extended Query Table at 0x0040
[    2.150000]   Amd/Fujitsu Extended Query version 1.1.
[    2.160000] number of CFI chips: 1
[    2.180000] 4 ofpart partitions found on MTD device 1c000000.nor-flash
[    2.200000] Creating 4 MTD partitions on "1c000000.nor-flash":
[    2.210000] 0x000000000000-0x000000030000 : "u-boot"
[    2.220000] 0x000000030000-0x000000040000 : "u-boot-env"
[    2.230000] 0x000000040000-0x000000050000 : "factory"
[    2.240000] 0x000000050000-0x000000800000 : "firmware"
[    2.260000] 2 uimage-fw partitions found on MTD device firmware
[    2.270000] 0x000000050000-0x0000001713ec : "kernel"
[    2.280000] 0x0000001713ec-0x000000800000 : "rootfs"
[    2.290000] mtd: device 5 (rootfs) set to be root filesystem
[    2.300000] 1 squashfs-split partitions found on MTD device rootfs
[    2.310000] 0x000000390000-0x000000800000 : "rootfs_data"
[    2.330000] libphy: mdio: probed
[    2.340000] switch0: Atheros AR8327 rev. 2 switch registered on mdio-bus
[    2.350000] Atheros AR8216/AR8236/AR8316: probe of mdio-bus:00 failed with error -22
[    2.370000] ralink_soc_eth 10100000.ethernet: incorrect phy-mode -22
[    2.380000] ralink_soc_eth 10100000.ethernet eth0: ralink at 0xb0100000, irq 5
[    2.400000] rt2880_wdt 10000120.watchdog: Initialized
[    2.410000] TCP: cubic registered
[    2.410000] NET: Registered protocol family 17
[    2.420000] bridge: automatic filtering via arp/ip/ip6tables has been deprecated. Update your scripts to load br_netfilter if you need this.
[    2.450000] Bridge firewalling registered
[    2.460000] 8021q: 802.1Q VLAN Support v1.8
[    2.470000] VFS: Mounted root (squashfs filesystem) readonly on device 31:5.
[    2.490000] Freeing unused kernel memory: 148K (8033b000 - 80360000)
[    3.310000] init: Console is alive
[    3.320000] init: - watchdog -
[    4.330000] init: - preinit -
[    4.750000] 8021q: adding VLAN 0 to HW filter on device eth0
[    4.790000] random: procd urandom read with 7 bits of entropy available
Press the [f] key and hit [enter] to enter failsafe mode
Press the [1], [2], [3] or [4] key and hit [enter] to select the debug level
[    8.080000] jffs2: notice: (299) jffs2_build_xattr_subsystem: complete building xattr subsystem, 0 of xdatum (0 unchecked, 0 orphan) and 0 of xref (0 dead, 0 orphan)                                                                      found.
[    8.120000] mount_root: switching to jffs2 overlay
[    8.150000] procd: - early -
[    8.160000] procd: - watchdog -
[    8.940000] procd: - ubus -
[    9.960000] procd: - init -
Please press Enter to activate this console.
[   10.930000] NET: Registered protocol family 10
[   10.940000] ip6_tables: (C) 2000-2006 Netfilter Core Team
[   10.970000] Loading modules backported from Linux version master-2015-03-09-0-g141f155
[   10.980000] Backport generated by backports.git backports-20150129-0-gdd4a670
[   11.000000] ip_tables: (C) 2000-2006 Netfilter Core Team
[   11.020000] nf_conntrack version 0.5.0 (959 buckets, 3836 max)
[   11.070000] xt_time: kernel timezone is -0000
[   11.110000] cfg80211: Calling CRDA to update world regulatory domain
[   11.170000] cfg80211: World regulatory domain updated:
[   11.180000] cfg80211:  DFS Master region: unset
[   11.180000] cfg80211:   (start_freq - end_freq @ bandwidth), (max_antenna_gain, max_eirp), (dfs_cac_time)
[   11.200000] cfg80211:   (2402000 KHz - 2472000 KHz @ 40000 KHz), (N/A, 2000 mBm), (N/A)
[   11.220000] cfg80211:   (2457000 KHz - 2482000 KHz @ 20000 KHz, 92000 KHz AUTO), (N/A, 2000 mBm), (N/A)
[   11.240000] cfg80211:   (2474000 KHz - 2494000 KHz @ 20000 KHz), (N/A, 2000 mBm), (N/A)
[   11.250000] cfg80211:   (5170000 KHz - 5250000 KHz @ 80000 KHz, 160000 KHz AUTO), (N/A, 2000 mBm), (N/A)
[   11.270000] cfg80211:   (5250000 KHz - 5330000 KHz @ 80000 KHz, 160000 KHz AUTO), (N/A, 2000 mBm), (0 s)
[   11.290000] cfg80211:   (5490000 KHz - 5730000 KHz @ 160000 KHz), (N/A, 2000 mBm), (0 s)
[   11.310000] cfg80211:   (5735000 KHz - 5835000 KHz @ 80000 KHz), (N/A, 2000 mBm), (N/A)
[   11.320000] cfg80211:   (57240000 KHz - 63720000 KHz @ 2160000 KHz), (N/A, 0 mBm), (N/A)
[   11.380000] PPP generic driver version 2.4.2
[   11.400000] NET: Registered protocol family 24
[   11.440000] PCI: Enabling device 0000:01:00.0 (0000 -> 0002)
[   11.450000] ieee80211 phy0: rt2x00_set_rt: Info - RT chipset 3593, rev 0402 detected
[   11.470000] ieee80211 phy0: rt2x00_set_rf: Info - RF chipset 000d detected
[   11.490000] rt2800_wmac 10180000.wmac: failed to load eeprom property
[   11.500000] ieee80211 phy1: rt2x00lib_request_eeprom_file: Info - Loading EEPROM data from 'soc_wmac.eeprom'.
[   11.520000] rt2800_wmac 10180000.wmac: Direct firmware load for soc_wmac.eeprom failed with error -2
[   11.540000] rt2800_wmac 10180000.wmac: Falling back to user helper
[   11.640000] firmware soc_wmac.eeprom: firmware_loading_store: map pages failed
[   11.660000] ieee80211 phy1: rt2x00lib_request_eeprom_file: Error - Failed to request EEPROM.
[   11.680000] rt2800_wmac: probe of 10180000.wmac failed with error -11
[   19.590000] 8021q: adding VLAN 0 to HW filter on device eth0
[   19.610000] device eth0.1 entered promiscuous mode
[   19.620000] device eth0 entered promiscuous mode
[   19.650000] br-lan: port 1(eth0.1) entered forwarding state
[   19.660000] br-lan: port 1(eth0.1) entered forwarding state
[   21.660000] br-lan: port 1(eth0.1) entered forwarding state
[   80.950000] random: nonblocking pool is initialized

I would like to be able to use OpenWrt firmware in this device....please some help!

There is very little information on this device https://wiki.openwrt.org/toh/trendnet/tew-692gr and I'm guessing that not much if any testing has been performed on it.

The logs seem to show that the relevant hardware is being detected, but as you see there are errors, and there is no reference as to what these error mean, at least not that I have found. I have a device that has errors and I've not found or had any answers.

Unless you are lucky enough to find someone else that has one running successfully then your best chance is to open  a ticket. https://dev.openwrt.org/newticket

I assume that you have made no other settings changes than enabling the wifi?

You may to consider collecting information like you can see on other wiki pages, take photos, links to factory firmware and the source code if it is GPL and available, factory firmware boot logs with a serial cable connected, bootloader type and version, confirm the chipsets, etc etc.

It is booting, also failsafe mode is ok but all tries to reach the Router via LAN are failing, so I decided to enable WiFi unluckly...

The only connection available is serial. Router is no more layer 2 reachable....
I've openned a ticket.

With older images errors were different:
[ 2.390000] ralink_soc_eth 10100000.ethernet: incorrect phy-mode -22
[ 2.400000] ralink_soc_eth 10100000.ethernet eth0: ralink at 0xb0100000, irq 5

Thanks Xotic750.