one computer on network keeps losing internet connectivity

I have a wired home network with three computers sharing a
cable modem. I do not have a file server. Everything has
worked fine until recently when one of the three computers
(running XP) started losing internet/email connectivity.
The other two continue to have it. This always happens
after the computer has been turned off and then
restarted. I have always been able to reestablish the
connection on the on the one computer by running the
Network Connection Wizard. This is now happening almost
every time the computer is switched off. I switched a
couple of the wires leading from the router thinking it
was perhaps the router, but that had no impact. Could it
be the wires? Something wrong with the specific computer?
Any other ideas? I would really, really
appreciate any help or ideas.