Not quite sure what you're trying to do: If you want to access one AOL account from two different computers, you need a dial-up connection and the appropriate software on each computer.
If all you want to do on one of the computers is read and send e-mail, you can use any account (it doesn't have to be AOL) to access the web, and then go to the AOL UK site (click here) and sign on to your account there.
You need to run ICS (Internet Connection Sharing) on both computers. Go to the computer that directly connects to the computer; go to Start, Control Panel, double-click Network Connections, in Network Tasks on the left side of the screen, click "Set up a home or small office network". Then just follow the instructions given by the Network Setup Wizard, which will appear.
The exact procedure after this may vary, but you shouldn't have any problems. If you do, come back and I will try to help you further.