Hm.. but this is not a modem, it's a router. Routers manage connected PCs via allocating IP numbers.
With a modem, it can only have one straight connection, and in that case you would have to run the setup disk on each. With a router, the router takes over the connection management to AOL, i.e. stores your password etc.
Are you plugging in the laptop to the router or relying on wireless? I'd start with the wire in so that you can eliminate the WIFI as a problem. You then need to ensure that the router is set up to run DHCP (it's the service allocating the IP numbers) and that the laptop is set up to receive the IP automatically.
Plenty of things can go wrong with the set up, but once running, it's wonderful to have the network connection on all PCs.