Anyways after disabling several add-ons one by one...I thought I would try disabling Avast Free Edition to see what would happen...it solved the problem. So obviously the problem is not Firefox but Avast.
You cannot disable Avast to actually check for this problem; you would actually have to uninstall Avast since the Avast drivers are still installed on your machine. So your test really wasn't valid.
Did disabling the add-on's one-by-one resolve the problem? You mentioned that disabling your FF add-on's one-by-one only identified one add-on as being an issue.
I agree with a poster above that a clean install of FF 3.6.8 is your best option, esp. if trying FF Safe Mode gave you no results. Upon reboot, FF does an add-on compatibility test...it's rather quick, so keep your eyes on the monitor.
Do you have any other security software on your machine (current or previously
) including AV and firewall (FW)? You mentioned that you now have Avast Free 5.0.594. What this an upgrade or a clean install? Please also give me your OS (32 or 64 bit). Perhaps I can identify if something is conflicting with Avast.