why not install winXP on the second computer? that would certainly solve your connectivity issues.
the only other way to access the other computer would be to disconnect it from the switch, buy a crossover cable and connect the two computers via the ethernet cards. winXP will handle that, you won't have to install winXP on the second computer and i think you can get a crossover cable for like $10.
of course, those more knowledgable on networking might have a better solution for you, but i don't think win98 will work - or it will work intermittently, kind of like when it wants to.