There are number of ways that this can be done... and some of them rely on the watchfulness of your ISP. A couple years ago when i first got DSL, the ISP wasn't watching closely and getting two computers on the net was as simple as setting the second computer to use the same TCP/IP gate way and DNS servers and turning on DHCP to grab an IP address. Now a days, the most effective way to do what you are doing is... I'm sorry... a proxy. Using a proxy, as long as the primary computer is logged on using the username and password, the proxy hides the second computer with a non routable IP address. To the ISP the internet requests are coming from one computer. WinProxy is a good solution for this...
The final suggestion is to upgrade to an always on connection... DSL, Cable modem... and just lease another IP address from the ISP. The are usually about $5 extra.. The speed at which you connect and the convience of not taking up a phone line can't be beat...