Hello Ian,
Did you enable ICS (Internet Connection Sharing) on the XP system that is connected to the Internet? If you haven't already, you can either run the Network Setup Wizard or do a manual configuration. You only need to enable ICS on one computer, the one that is going to act as the ICS server.
Keep in mind that in order for the client, or your other computer to get its Internet connection, the computer acting as the ICS server must be turn on.
If you haven't already, please see:
http://www.practicallynetworked.com/...rksetupwiz.htm
Then on your other machine you can follow these steps:
http://www.practicallynetworked.com/.../clientwiz.htm