Check the bars on the network (anything less than "fair" is unacceptable)-you may need to bring notebook closer to router.
This can occur if encryption key is not the same (keys are usually changed once a day or so by router depending on setting), Or if there was a forced wireless browser election.
(Different computers on same network may think they are both master browsers and force an election- resulting in loss of internet connection)
Are you using a "secured" network? If your connection shows up as secured you need to enter your key. If "unsecured" network, or key already on Vista system, try following:
Power off ALL computers power down router and modem.
After a few minutes, power on modem, then power on router, then power up Vista computer, then XP systems
If you are set up for either a WEP or WPA secured network , and do not know your key this can be retrieved of the XP machines through the wireless config wizard, or you can reset your router to its default settings by pushing the reset button on the back with either a paperclip or push pin, and then connecting to the "unsecured" Linksys network.
If you are set up for MAC filtering through the router you must add the IP for the new computer/disable MAC filtering, or reset router to default.