When you try to start firefox, an error about firefox’s profile being missing is shown and firefox won’t start at all.
Cause & Solution —
There are many causes for this problem. So your first step to do is to google about it and trying some of the solutions there.
If the problem still persists, then it may because there is an error with your user account, possibly involving permissions to your firefox profile. Change your account to an administrator account, then try opening firefox again. If it works then just create and use a new user account and remove the old one.