Are you receiving any error messages? Have you contacted your email provider to see if they are having problems? Please share more information.

I can go to the email provider and get emails, as if I was out-of-town, but not on the Mozilla/thunderbird site where my files are.

Ok, then I presume there may be an error message or other indicators to share?

No error messages or other indicators. The emails simply do not come in. When I click on "get messages," the little bar illuminates, but then goes out in a few minutes with nothing downloaded.

Please visit Help > Troubleshooting Information and find "Mail and News Accounts". Please post what you see there.

These problems also tend to be antivirus related. Please state the AV software being used.