Have you tried to change the encryption setting on the wireless adapter of the problem computer?
1) Go to Start and click on Control Panel.
2) Control Panel window will appear. Double click on Network Connections.
3) Network Connections window will appear. Right click correct Wireless Network Connection by identifying correct wireless adapter and click Properties.
4) Wireless Network Connection Properties will appear. Click Wireless Networks tab.
5) Tick Use Windows to configure my wireless network settings. This will change the wireless adapter management from wireless adapter configuration software to Windows XP built-in wireless configuration tool. Click Add to create preferred wireless network.
6) Wireless Network Properties window will appear. Here is the place you key in your wireless network information, it must match with the settings you set on wireless router. If not, you will fail to join the network.
7. Ensure you're using the correct Encryption on the adapter.