The x86_64 images have the kernel modules for the most common ethernet cards pre-installed, but anything more exotic might need installing (imagebuilder/ online-imagebuilder can help with that, once you know what's to be added) - or packaging (from the mainline kernel), in case of more rare stuff.
In contrast to OpenWrt, a typical general purpose linux distribution has a lot more (~everything imaginable) preinstalled, making this easier to debug - so run a live linux USB stick of your favourite distribution and run lspci -knn there, to find out what you need. While there are other approaches to debug this from plain-OpenWrt, without any detours to other linux distributions, this tends to be the quickest and easiest.
Keep in mind that a system of ~2010 vintage will likely have an idle power draft of around 75+ watts (which might be fine for a client, used sparely, but is less impressive for 24/7 usage of a router), while more modern (>= haswell or >= baytrail-d) might get away with 5-15 watts, which can quickly pay for itself within short time (less than a year, even if you buy a new device). So reconsider if running this device makes sense, economically and ecologically. Tips for getting cheap used x86-based firewall with full Gbit NAT (a PC Engines APU) if you are in the US (especially in the later parts of it) has a few examples which often sell for under 50 EUR/ USD (used), but get away with less than 15 watts.