Seems you are getting kicked from all sides at the moment!
I'm thinking that, although Mozilla claim this version can be installed over the top of an existing version, that may not be correct in all cases. Mine froze the first couple of times I used it, but behaves itself now.
Finding 2 profiles under the Programs folder concerns me a little - not unheard of, but a bit unusual. Try the following method of backing up - I want to make sure we don't lose anything.
Download
MozBackup. Double click the downloaded file (named
MozBackup-1.4.10-EN.exe) to install.
Now run MozBackup (Thunderbird must be closed to allow a backup to be made), select
Thunderbird when prompted, accept the default location for the backup (it will be saved in your My Documents folder) and answer No to password protection. On the next screen check anything you can except 'Accounts settings only'. Click Next and wait while the backup is performed, then click Finish.
Repeat this for the other profile if there is more than one showing in the box.
(If you use the Firefox browser then you can use MozBackup to backup this profile, too).
Next, download
CCleaner - you want the Slim build at the bottom of the page. Install it.
Then:
1. Uninstall Thunderbird via Add/Remove Programs and reboot the computer.
2. Run CCleaner, go to Options and click the Settings tab, then click Advanced. Uncheck the box against 'Only Delete Files in Windows Temp Folders Older than 24 Hours' and click OK. Go back to the Cleaner tab, make sure there are no browser windows open and click Run Cleaner. Close the CCleaner window when finished and reboot again.
Please note that running CCleaner will force you to enter login and password details for any sites which require them. Make sure you know them!3. Install Thunderbird 3.1.6 again, choosing not to set up any accounts if asked. Close TBird and run MozBack again, but this time select Restore and restore the profile backup. See if Thunderbird behaves itself this time.
If you get stuck with any of that then please shout up and we will sort it out.
Let me know how it goes.