It could be many things. I would try it for starters:

Try Firefox Safe Mode to see if the problem goes away. Firefox Safe Mode is a troubleshooting mode that temporarily turns off hardware acceleration, resets some settings, and disables add-ons (extensions and themes).

If Firefox is open, you can restart in Firefox Safe Mode from the Help menu:

• Click the menu button , click Help and select Restart with Add-ons Disabled.

If Firefox is not running, you can start Firefox in Safe Mode as follows:

• On Windows: Hold the Shift key when you open the Firefox desktop or Start menu shortcut.
• On Mac: Hold the option key while starting Firefox.
• On Linux: Quit Firefox, go to your Terminal and run firefox -safe-mode
  (you may need to specify the Firefox installation path e.g. /usr/lib/firefox)

When the Firefox Safe Mode window appears, select "Start in Safe Mode".

If the issue is not present in Firefox Safe Mode, your problem is probably caused by an extension, theme, or hardware acceleration. Please follow the steps in the Troubleshoot extensions, themes and hardware acceleration issues to solve common Firefox problems article to find the cause.

To exit Firefox Safe Mode, just close Firefox and wait a few seconds before opening Firefox for normal use again.

When you figure out what's causing your issues, please let us know. It might help others with the same problem.

Do you have the Firefox icon on your quick launch? Right click on it, and select Open New Window. Sometimes this works. If it opens, close it by Menu > File > Exit.

It is possible that the Firefox window is off screen and not visible.

Can you open the system menu via Alt+Space and resize or move the window?

You can try to rename/remove xulstore.json and if present delete localstore.rdf in the Firefox profile folder with Firefox closed.

Location used for the main profile that keeps your personal data in "AppData\Roaming" (Root Directory on about:profiles).

• C:\Users\<user>\AppData\Roaming\Mozilla\Firefox\Profiles\<profile>\

"AppData" (XP: Application Data; Mac: ~/Library; Linux: ~/.mozilla) is a hidden folder.

• http://kb.mozillazine.org/Show_hidden_files_and_folders