OK, I now can get to the wireless router (I can access the set up) and I can ping the IP, but can't get internet connection. I rebooted the router, wireless and computer.
Might just be easier to grab a wireless adapter rather than spending ages trying to get it working. Here in the UK, you can get ones off amazon for about £5.
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.