I click on the inbox in the account that does not work and Thunderbird goes into endless loop.

What does 'endless loop' mean exactly?

When I start up Thunderbird the program downloads all the new emails for three of my the four email accounts. I click the down arrow next to Get Messages and then click Get All New Messages and the account that's giving me trouble still doesn't download any new messages. I then click the "inbox" icon just under the account name in the left hand column of the Thunderbird window and in the box at the top left corner of the Thunderbird window the dot goes back and forth with the words "Inbox - myaccountname" to the right of the back and forth dot. This dot will go on for over ten minutes does not give any error messages. The other accounts have downloaded the new emails. I borrowed another computer and it will download the new emails in the troublesome account. Thanks for the quick response.

Is this a Gmail account, and you're subscribed to 'All Mail'?

These are not Gmail accounts. The emails accounts are for four websites hosted by R4L. How do I check if the email accounts are "subscribed to 'All Mail' "?

'All Mail' is a Gmail thing, so it isn't relevant for you.

What is your anti-virus software?

Anti-virus is Norton. Can I send you a private email. It will be a screen shot that contains all my email addresses. It's of Preferences>Privacy & Security > Saved Passwords window.

Can I send you a private email.

I don't think that's needed at this time.

Try to start Windows 10 in safe mode with networking enabled. Does the problem go away?

Windows safe mode disables anti-virus software among other things. This is a troubleshooting step, not a solution.

I went into safe mode with networking. Opened Thunderbird. The problem account will still not download new emails and if I click on the indox for that account I get the dot moving left to right. Also the three other accounts, when I click on Inbox for each account to check and see if they were working, I got an error message "Thunderbird failed to connect to server imap.theaccountname.com."

Are you using WLAN? This may not work in safe mode. A wired connection would be preferred.

I am using a WLAN. This is a laptop and it does not have a port for a wired connection or I would be using it. If safe mode will not work with a WLAN and I got an error message with the other three emails accounts, but I did not get the error message with the account I am having trouble with might Thunderbird not be going and looking for the ISP sever for the troublesome account?

See if this helps. I haven't tried it. https://community.spiceworks.com/how_to/125006-how-to-restore-wi-fi-connection-in-windows-10-safe-mode

I tried the link you sent me. Thanks for the getting it. In the information in the link, step 4 talks about clicking Expand. I believe that is now a globe like icon. It brings up the Show available networks window. There are no networks in the windows. There is nothing to click on while in safe mode to choose or connect to a network.

Did you start Windows 10 in safe mode with networking enabled?

Yes, I started windows 10 in safe mode with networking enabled. I did it a couple of times to make sure.

Without Windows safe mode, there is no proof that anti-virus software is the culprit. However, often times it actually is.

These are some generic suggestions to avoid problems with anti-virus software.

Create an exception in your anti-virus software for the Thunderbird profile folder, so that the anti-virus real-time scanner will not scan it. https://support.mozilla.org/en-US/kb/profiles-where-thunderbird-stores-user-data#w_how-to-find-your-profile

Don't let your anti-virus software scan incoming and outgoing messages.

Don't let your anti-virus software scan attachments.

Don't let your anti-virus software intercept your secure connection to the server.

Remove any add-ons your anti-virus software may have installed in Thunderbird.

Keep it working. http://kb.mozillazine.org/Keep_it_working_-_Thunderbird

And last but not least, backup your Thunderbird profile on a regular basis. https://support.mozilla.org/kb/profiles-where-thunderbird-stores-user-data#w_backing-up-a-profile