Exactly. The router fools AOL into thinking you are on 1 IP address using NAT. It accepts net requests from all your pc's which will all have different LOCAL ip addresses. The router then sends these off to AOL using the 1 IP address it gets from AOL. When the pages come back they are routed back to the originating pc.
Just make sure DHCP is turned on in the router and you should be ok.
You can make sure this is working properly but typing 'ipconfig' at a dos prompt on any of your pc's.
It will tell you ip address assigned to you by router. For example I get 192.168.0.1 my flatmate might get 192.168.0.2
Can you confirm modem is plugged into router and not through another pc. If using router you should NOT be using ICS (internet connection sharing).
Boo!