Prior to this problem did you ever get Firefox prior versions to work on your system. Or is this the first time you're dealing the browser? You might have to go into the hidden folder Application Data files and make sure all reference to Mozilla Firefox is removed off the system. This means to uninstall the browser and the go into hidden folder but turning on view hidden folders. One more way is to go into safe mode under admin logon name other than what you use. Then backup your desktop icons, links or anything you need to keep for browsing. Then you need to delete your profile on the system this will bring the system back to the state you had when you first build your profile. Note some applications might have to be re-installed as they might now show up in all programs menu. They will be still on the HDD but the links pointer will be gone or not. So you have two choices clean the system from all reference to Mozilla Firefox or delete your profile under safe mode, this would get rebuild by OS next time you login.
Firefox has it own method for deleting the profile for it but you have another issue where that won't help. You can always redo the entire system OS, but that takes time unless you have a system backup clone image that was working prior to this problem?