it sounds like the good computer is on a static IP address, you will have to setup the other computer (there are no bad computers!!!) with the same IP address info. To do this you will have to get your tcp/ip properties:
right click on My Network Places, select properties
double click on the adapter name
click properites
highlight the Internet Protocol (TCP/IP) and then click properties
you will then see a box with tcp info, just copy the addresses (IP, subnet, gateway, dns) from the good one to the other one.

good luck, let us know if it works

cheers
Luke