check the icon link and make sure it points to the correct exectuable. (or try to run firefox from your "root" account. If that works, then it could be something is wrong with the user account.)

Have you tried running the firefox application from a terminal console?

its the file "firefox". You run it by entering its name in command line. For example, if you're already in the folder, type ./firefox, and press enter. (In this case you must include the "./")