Wireless adapter may not be getting an IP address from the router automatically, that is to say, XP computer may be set up for a locked static IP address that is out of range for the router.
Start>Settings> Network Connections>right-click on your wireless connection>Properties>General Tab>Internet Protocol>Properties>"Obtain an IP address automatically">"Obtain DNS server address automatically"
Also, make sure "Client for Microsoft networks" is checked (as well as "Internet Protocol (TCP/IP)"
If/when this is setup and you still have problem, run the network setup wizard... only after the above is correct.