If I understand correctly, you are trying to provide LAN connectivity to a computer on a Wireless LAN. However, your computer has no wireless capability.
In this case, you can use a wireless router such as the Cisco/Linksys WRT54 family, install a new firmware that is based on Linux such as DD-WRT and turn it into a Wireless access point for wired-only computers. I had to do this for a computer which could not have wireless connection. Once the router was setup as a GATEWAY, with the proper credentials to connect to the wireless network, it was acting as a gateway, sharing the same IP address space, and providing full connectivity to the Internet.
Another reason to do this is that my wife's computer, running Vista, sometimes disconnects itself from the WLAN, if left on for too long without networking activity. And in this case, the only solution is to save everything and restart, as it will not see the wireless access point anymore. Of course, I don't have such problem under Linux. My solution tothis is to install this king of gateway, which takes care of the wireless connection, and becomes a simple Cat5 cable connection to my wife's PC, not even realizing it is using a wireless connection.
Google for DD-WRT. There is also another firmware named Tomato which can be used to provide such capability.
You can find more here: http://www.dd-wrt.com/wiki/index.php/Client_Mode_Wireless