Whoops, that's not good. Do you recall what the last thing was that Firefox was doing before this problem started?

One initial guess:

If Firefox was trying to run its Refresh procedure but didn't complete it normally, do you see a folder on the Windows desktop named Old Firefox Data? If so, please check inside to see whether it has a semi-randomly-named folder with recently updated files inside. We'll need to to restore your lost settings.

You need to locate the profiles.ini file and delete this file or use the Profile Manager to create a new profile.

See:

• https://support.mozilla.org/kb/how-run-firefox-when-profile-missing-inaccessible

This issue is caused by a problem with the profiles.ini file or with permissions/ownership of involved folders/files.

You can use one of these to make Firefox create a new default profile or recover an existing profile:

• Delete the profiles.ini file to make Firefox create a new (default) profile
• Use the Profile Manager to create a new profile
  If you still have an existing profile then click "Choose Folder" in the Profile Manager and browse to the location of a lost profile to recover this profile
  https://support.mozilla.org/kb/Managing+profiles

You should find the profiles.ini file in this hidden location:

• Windows: %AppData%\Mozilla\Firefox\
  *C:\Users\<user>\AppData\Roaming\Mozilla\Firefox\
• Mac: *~/Library/Application Support/Firefox/
• Linux: *~/.mozilla/firefox/

If clearing the profiles.ini file isn't working then also check the location of the cache files.

• Windows: *C:\Users\<user>\AppData\Local\Mozilla\Firefox\Profiles\<profile>\
• Mac: *~/Library/Caches/Firefox/Profiles/
• Linux:*~/.cache/mozilla/firefox/

You can also try to rename/delete the Mozilla\Firefox\ folder in both above mentioned locations (main, cache).

• http://kb.mozillazine.org/Profile_Manager
• https://support.mozilla.org/kb/Managing+profiles
• http://kb.mozillazine.org/Profile_folder_-_Firefox