"route" command output has told me you have no default route.
"nslookup" command output has told me you have no DNS servers configured, or DNS servers configured which are not accessible on this LAN.
"ping" is irrelevant, due to the output of "route".
"wget" is irrelevant, due to the output of "route".
Please check your configuration found under "/etc/conf/network". Here an example of mine;
config interface 'vlan10'
option type 'bridge'
option proto 'static'
option netmask '255.255.255.0'
option ip6assign '60'
option gateway '192.168.10.254'
option ipaddr '192.168.10.240'
list dns '192.168.10.1'
option stp '1'
option ifname 'eth0.10 gre4t-trunk0.10'
Note:
option gateway
list dns
Edit: You really are asking questions regarding "using" OpenWRT, not development specific questions. Faster replies will most likely be found at the forum "Installing and Using OpenWRT"
The key to getting the U-Boot recovery web page turned out to be setting the IP address of the connected computer to 192.168.1.10. It wasn't enough to use some other address on the same subnet!
After this, I was able to upload the image again via the recovery web page, and after that ssh in (without a root password).
From there, it was possible to install luci. But first, I had to add DNS settings and a gateway to the lan interface, in /etc/config/network . For example:
option dns '8.8.8.8 8.8.4.4'
option gateway '192.168.2.1'