The main problem with using anything other than the prescribed modem is that it will be touch and go whether it works. The most important factor is the MTU size, this needs to be set at 1400 and usually by default it is something slightly over this setting. You need to get into yuor router settings and set the MTU to the correct size before you even start to try anything else. Overall it is easier to use the prescibed routers and they have all the trouble shooting and settings ready if you need them.
I use this excellent router with my crap AOL Platinum account (can't wait until the 12 months are up so I can switch to another ISP!).
The 1400 MTU settings mentioned earlier - and other settings - can be found on an AOL advice page on home networking in the AOL site (start at Discover AOL on your AOL Welcome page). Using these my set up went well. Although they don't support the Linksys router one page I found did give advice about the settings on routers in general and these worked fine.
Sadly I can't find an AOL page to post this morning as the links on their home networking advice pages aren't working today! If I spot it I'll post later this morning.
Rest assured the router will work with AOL okay once you get the right settings in. Until I got the right settings in my router seemed as dead as a dodo too. When all works and you're online you'll see a total of 5 green lights on the router. One for the power, one for the main wired link to a desktop, one for the wireless field, one for the DSL (i.e connection to the phoneline or cable) and one on the far right goes from red to green once surfing. Some of the green lights blink when there's Net activity.
Best of luck. Once it works you'll never leave the sofa/bed/garden chair to surf again (except to re-boot the router when the signal drops now and again).