I can't explain why it isn't working for you, but does so for me.
Disabling Avast doesn't pin down the cause, try disabling a shield at a time, start with the web shield. However, you would need to first check that there is an update on the thunderbird website.
What I don't understand is what you said - "If I use "check for updates" it also showed no updates (says Thunderbird is up to date) " message - Then thunderbird has to have been getting through, otherwise how would thunderbird know that there is no update beyond what you have.
You didn't answer my question:
Are you using any other security based software ?