Hi,
Welcome to the forums!
I'm not sure why you would be unable to add another email account/address to your TB client successfully, but if you're okay with starting with TB from scratch, what you'll need to do is, once again, uninstall TB. Then you'll have to delete your TB profile. (Simply uninstalling TB doesn't remove that folder; that's why every time you re-install TB your info is there again.)
You might want to read
this thread, specifically the second post (by Big Dan) and see if that's enough information for you to do it. (The thread is about editing the profile, but he provides information on how to delete it.) If not, go to
this Mozilla page about where to find your TB profile. Simply highlight the profile folder and delete it. May as well empty your recycle bin while you're at it. Then re-install TB and it should treat you like a brand new customer!