It looks like you've configured TB's multi-user environment.
Due to my own setup I can't reproduce that.

The reason that the problem occurs again after reinatstalling everything is that TB doesn't delete your message base etc.

When nobody gives you an easier workaround, you can do this.
1) Find your mail directory, the default location is somewhere in documents and settings (don't know exactly where, as I keep mine somewhere else)
2) Uninstall TB
3) Move your mail directory to some other location
4) Install TB again and configure all accounts (give them the same name as before), but don't start to collect mail.
5) Close TB
6) In the old (moved) mail directory you'll find subdirectories for all three of your accounts. Delete from these subdirectories the account.cfg files.
7) In your old (moved) mail directory you'll find a couple of files (don't look in the account directories), delete those except for the address books (the .abd files), when you were using common filters you can keep account.srb, when you were using common folders you can keep account.frb
8) After manipulating your old (moved) mail directory, copy it on top of its original location.
9) Start TB and see whether everything is back again.