Remove Firefox again, and also move or delete the C:\Program Files\Mozilla Firefox folder, and the C:\Documents and Settings\{username}\Application Data\Mozilla\Firefox folder.
This will delete or move all your preferences, your profile, extensions, themes etc, so if you want to keep the move the folders somewhere else, like the desktop, rather than deleting them.
Then reboot, and install
CCleaner's Issues function to remove anything related to Firefox it finds left over in the registry, such as file associations, short-cut references etc.
Be careful when using CCleaner and backup your registry before you clean anything.
Then reboot again.
Then reinstall Firefox and see if it works with a fresh new profile, no extensions etc.