Your "profile" is probably broken. This is where addons and settings and history and bookmarks is saved. The profile won't get removed when you uninstall Firefox because it's saved somewhere in your user's directories and not in "C:\Program Files". When you then reinstall Firefox, you'll be back on your old profile.
There's a way to start Firefox in a "profile manager" mode, where you can create alternative profiles and switch what the default is. I don't remember how that works, so you'll have to google that.