Since you have read other topics, I guess you could have said what you have done to try and remedy this. Starting with the usual suspects, firewall blocking avast's web shield, etc. etc.
Disabling avast is the worst possible option, disabling the web shield would be a stop gap whilst retaining the other resident protection, so the lessor of two evils.
I would Imagine that the AOL browser/interface isn't even monitored by the web shield, as it uses a different, proprietary protocol, so that would be why that gets through. I would imagine if you tried visiting a https page that would get through also as the web shield doesn't monitor https (secure encrypted) traffic.
If this is also correct then it sounds like the web shield itself is being blocked.