I feel myself quite incompetent so solve Mozilla and/or Thunderbird problems with avast. At least, if you uninstall AVG and then install avast! it must work without problem. Anyway, can you confirm:
- you checked the option ‘save password’ into email accounts
- you checked the option ‘save password’ into smtp authentication
- you checked the right option to the Internet connection (Internet Settings of the browser)
- your avast! configurations (Update (Advanced) options) define correctly the way you connect the Internet (dial-up or DSL)