back in the day there was a program called Laplink, that came with a crossover cable, and a simple program..I've still got it (it's probably older than some of the posters here..early 80's..;).
If those are RJ45 connections (in the US, 6 little gold strips instead of the RJ12's 4), that's usually an ethernet connection (or a digital phone..but not likely). The trick is to get a network connection, if you have 98, I think you can set up what's called a peer-to-peer network (there's 2 version of 98..SR1 and 2..2 fixed bugs in SR1)
If you set up a peer network, you can share drives across it, and transfer with ease..even share the printer, if you like.
granted, the person above me has the simpler solution, but the possibility is there. From what you describe, the equipment is there..you get a faster transfer rate (10 or 100mbps, depending on the card and drivers), but USB still transfers in the Megabit rate. Good luck- I have a burner in each computer, so I tend to use that..another option, if you have one..good luck.

I wish I'd said that.. The Staircase Wit

anahl nathrak uth vas betude doth yel dyenvey..;)