Since Avast and AVG are now one company, I'll take a stab in the dark here (as I have AVG) - go in to email settings and see if there is an option for NNTP - if there is, turn it OFF. That is one place AVG screwed me when they first rolled out the Avast/AVG combo new engine.
The other thing is, go into the firewall, and I know this is a little risky, but change the options on Alt.Binz so all TCP and UDP ports are allowed in and out. Take a NOTE of what they are set to *BEFORE* you do this, because it may not be necessary and you can roll them back to their original settings.
Alt.Binz doesn't really use that many ports - what might get you is a news server with a non-standard port - but if it is 119, 443 or 563 they should already be open.
Hope that helps