So the TCP stack hasn't fallen over then, thats good :)
Sounds to me like you have got the wireless network key wrong, I assume you have windows XP!
XP is a pain because if you use the wrong network key to connect wireless it will connect and won't report any errors but you will not be able to use the connection and your router won't assign you an IP address (thats why your getting 0.0.0.0)
disconnect from the wireless network and then connect again and it should prompt you for the wireless key again, re-enter it and it should work OK
If you don't know the wireless key then you will need to use the other compuer that does work to login to the wireless routers admin pages to get it, if you need help with this post back with make of router.