As a test, could you try disabling the Avast "Mail Shield"? You probably can find it under Avast Settings, Active Protection category.

If Thunderbird can connect with the Mail Shield disabled, and you want to use this shield, then you need to set up Thunderbird to trust Avast's fake certificate for your web server. This article is for an older version of Avast but I suspect the steps for the current version are similar: Avast FAQ | Avast 2015: Warnings about invalid mail server certificates when sending and receiving e-mails.

Hmm, also, that is a rather old version of Thunderbird. Any reason you are not using Thunderbird 45?

I was mistaken about the Thunderbird version. I do have version 45.2.0

I have tried disabling "Mail Shield". That did not fix the problem.

When I search around for these error messages, there are some references to port 25 being blocked. That is an SMTP port, but most providers no longer use it, having switched to 587 with STARTLS or 465 with SSL/TLS.

Does your provider support a connection on either of those ports, or only on port 25?

Also, could you check Avast's application settings to see whether it allows Thunderbird to connect on whatever ports are supported by your mail service? https://www.avast.com/faq.php?article=AVKB25

I have POP3 email and it uses port 110 It has been the same for several years. Everything has worked fine until a couple of day ago. The only thing different was I updated to the latest version of Premier AVAST and I think that my problems started after that. I can still receive emails as before, but cannot send them. I get that error message 10060.

Yes, your outgoing mail, the SMTP protocol, is in a different part of the Account Settings dialog, probably toward the bottom of the left column. That's the area to find port 25 and maybe try an alternate connection method.

If the Avast article didn't help, you might try their forums to see whether there is a know issue working with Thunderbird.

You were correct about the outgoing server being port 25. The default server port was 587. I switched to that and I am now able to send emails. Thank you for your help. It is nice to have people like you to help us "rookies"