Do you get an error message or just a hang?You can find Avast! v6 instructions for setting up TB with gmail at http://forum.avast.com/index.php?topic=76915.msg636942#msg636942 ; others are similar. Also check Mail shield/Expert Settings/SSL accounts to be sure that nothing there got changed in the upgrade process.
What actually happens when you try to pick up mail? What are you using for a firewall? Make sure avastsvc.exe is allowed tcp out on port 995 if using ssl, port 110 otehrwise.