All you should have to do for the networking the two computer together is put a network card in both of the computers and use a different IP segment than the cable modems IP.   (like 192.x.x.x which is not a real world IP address)
On the (new) computer on the network, you can try to set the gateway IP to the IP of the phone networking card and see if you can get to the internet....?
If you have ME or 98se 0n the computer that has phone line network card, use internet connection sharing.  Add the service to the network card and the wizard should walk you through setup...