Best thing to do is ditch the AOL software on your computer and set up a router with your account details. You can then connect as many computers as the router will support to the internet at the same time. This is what I've done with my 3 computers.
If you're not sure how to set up the connection details on a router I would recommend the Netgear DG834G. This auto detects your line settings and all you have to do is enter your primary login name and password. Login name is actually the email address that AOL gave you initially.