You are using Norton Internet Security 2006, this is one of the main reasons why people have been going away from Norton as the issues it causes with XP and internet connection.
Trying to do everything with ONE product makes it a nightmare for troubleshooting issues like this, but as you have noticed the inbuilt Norton firewall is blocking your AOL connection.
My advice would be to completely disable the Norton firewall and ONLY use the Anti virus part of the product.
XP comes with an inbuilt firewall that will stop most issues.
The problem you are having is with the proxy server that is within Norton, normally for connection to the live update server. This is blocking your connetion to the AOL servers as it confusing your machine. Hence when you turn Norton off you can connect with AOL.
HERE (http://www.symantec.com/techsupp/files/lu/lu.html) is a patch for the live update service that MAY resolve your connection issue.
You may have to manually setup the AOL proxy server information within your browser. Here (http://webmaster.info.AOL.com/proxyinfo.html) is a list of proxy's used by AOL.
As you haven't mentioned which browser you are using I can only give advice for IE as I'm not familiar with AOL's browser.
Go to Tools > Internet OPtions > Connections Tab > LAN settings Button > Proxy information goes in the bottom box. Click OK and restart IE.
Hope this helps.