You might have better luck with buying a cheap $15-$20 USB to RJ45 ethernet adapter that supports Windows 10 and go that route. From system restore back to factory original non windows 10 OS, did this adapter run fine up until Windows 10 upgrade?
Its not uncommon for an older computer to not have drivers for Windows 10. I have a laptop myself that is running 7 and I went to accept the upgrade and it came back and told me that my chipset is too out of date to support 10. Windows 10 is not perfect for detecting and flagging all incompatible hardware/devices. To the OS it could say the Ethernet Chip initialized correctly with say a legacy driver, and yet be non functional.