Seacue, if you're going to use Thunderbird again on your new setup you might as well copy the thunderbird profile folder from the old computer to the new one, that will get you your settings, password and mail folders back on the new computer. For info:
http://kb.mozillazine.org/Profile_backup If you follow the instructions there but restore to your new computer you'll be up and running again.
You still won't know what the actual password was but you can still sort out that one later with the mail provider.
At least you can email them about it.
Note: Kwachon's solution is for lost Windows passwords, not e-mail account passwords!