ok so make sure you are using the right kind of cable to start with. If the XP computer is working and the 98 one is not you might have two different kinds of cable. One is called a crossover and the other is a straight through connection. You can test this by swapping the cables, if practical. This will also check to see if the one cable is just bad.
Next you need to make sure your settings in 98 are correct. here is a few things to check
1) does the computer see the lan card you are using? (in control panel, systems, hardware)
2) are the drivers up to date?
3) can you hook the modem directly up to the lan card and get internet?
4) can you see other network resources from the 98 computer? (ie the other computer)
5) when you look at the hardware do any of the system resources have a yellow or red flag next to them? This would indicate a problem that needs to be addressed.