That is a very old machine. Probably isn't worth upgrading to begin with.
A USB ethernet adapter should work for you. Chances are, the USB ports are 1.1 and not 2.0. You can plug a USB 2.0 device into a USB 1.1 port and it will work. You will not get USB 2.0 speeds though.
FX-8350 @ 4.7 cooled by H80, 32GB Mushkin Enhanced Blackline 2133, Asus Sabertooth 990FX, 2x Radeon HD 7850 2GB in X-fire, 500GB Samsung 850 Evo, 4TB Seagate, 3TB WD Black, 2x 1TB WD RED in RAID 0