are you getting an IP? (start --> run, and type 'cmd' from the prompt type 'ipconfig /all' )
Do you have WEP set?
Do you have DHCP set correctly in the router?
From ipconfig /all you should see
DHCP Enabled... yes
IP Address ... 192.168.1.101 (or something around there)
DNS Server... 68.2.2.2 something like that
Default Gateway ... 192.168.1.1
If you get an IP of 169.254.23.23 or something like 169.254.x.x it means you're not pulling an IP from DHCP. ie. you're not connecting to router correctly, or dhcp is not set correctly.
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If you need help with any of those points feel free to ask!
-- edit ---
Umm all of this was assuming your access point is also a router
Is it?
Or do you get an ISP IP on the working machine?