LAN network cable unplugged

I just installed a Linksys home router and a Belkin Wireless Network adapter on 2 different computers in the home. On the secondary computer that is receiving the wireless connection (Windows XP), the LAN network cable is unplugged. I am able to connect to the access point, I am unable to gain access to the Internet. I’ve read other answers to situations similar as this but I couldn’t find NIC in my Network Connections and I am not sure what all the cable talk is about!
Thanks so much for any help!