With both the XBox and PC on dynamic IPs, you're going to have problems, especially with Windows 98.
The cable modem does "dial-up", sort of. Every so often your DHCP lease will expire and it'll request a new IP (or a lease renewal) for you.
What I'd do if I were you, would be to make a gateway between the cable modem and your network; that way your sub-net can have static IPs and you can route traffic from anything through the gateway.
Probably the easiest thing for you would be to add an extra network card to your PC (a cheap 10MBit one
should do fine for the cable-modem side).
Then do:
cable wall socket
|
cable modem
| (cat5e)
PC (10MBit i/face with dynamic IP from modem)
PC (other NIC with static 192.168.1.1 (example) IP)
|
Hub/switch/whatever
| (cat6)
xbox (192.168.1.2 IP with gateway set to 192.168.1.1)
Then all you have to do is get traffic to route between the two interfaces on the PC (no idea if '98 can or does that), I use Linux on my gateway (pretty sure 2000/XP will do it too).
Cheers,
Ref.