As dobby said check the workgroup and also the ip range.
then check the ethernet port (network port or rj45 whatever you want to call it) is working.
then check the firewall settings
and if all else fails take the hard drive out of the xp pc and plug it into the vista pc as a secondary drive (set jumper to slave) and take the files you need directly.
Well, typically with network problems, the solution is to work at layer one (physical layer) and move upward. Are you positive that your NIC and Cat5 cable are working? I have had many NICs just die for no reason at all. Cabling can be suspect especially if it has been kinked or twisted a lot over time. Just thought I would toss out the easy ones first.
Try using DHCP instead.
Some routers are [insert homophobic remark here]
Do that by selecting "Automatically obtain IP address" in your tcp/ip protocol settings.
Also if you have zonealarm installed on the computer, make sure you add your network as a trusted zone.
Shutting it down still might not allow traffic through.