how long have you waited for the message?
after a fresh installation of TB, this may happen. Open TB, leave it open for a long time to see if that message can be cleared by itself. If not, the TB may not be correctly installed. then you may have to uninstall your current TB, and run the setup file again.
to backup thunderbird(emails and profile), locate the profile folder:
The character (~) refers to the current user's Home folder, so ~/Library is the /Macintosh HD/Users/<username>/Library folder.
then just copy this profile folder out, after a new installation, copy this folder back to the same location.