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The last time I checked (a few months ago) AOL were not fully supporting PS2 and Xbox online - they were going through beta tests. If this is still the case, you are unlikely to get online yet.
If, however, they have completed their tests and have fully launched support for the consoles, it may be your modem. Does it connect to a USB port on your computer? In this case you will need to get a network card for your PC (about £5-£15) and use a CROSSOVER cable to connect the PS2 to your PC. Note croossover - not straight cable. They look identical so I suggest you ask a member of Dixons, Currys etc. for the correct cable.
Once this is connected to your PC, go into Network settings on your PC and enter the 'properties' facility for your AOL connection. From there, click on the 'advanced' tab (far right tab) and enable ICS (Internet Connection Sharing). You may or may not be able to use the firewall while using the PS2, but try it anyway, if it doesn't work, disable the firewall.
Now, restart your PC (just to be safe, although I doubt there is a need for it) and switch your PS2 on while the PC is rebooting. DON'T try to go online yet though, wait till the PC has booted.
Connect to AOL on your PC then close all browsers down so your PC is not using the net but it's still connected.
When that is done, attempt a connection through your PS2. It should be recognised by the PC (which should kick in and start sharing data).
You should be online now.
Note that the above is the best method in your situation, but NOT guaranteed to work as AOL may still not be supporting PS2.
Give it a try though. If all else fails. Cancel AOL Broadband. What were you thinking? :P