Try:
Ctrl+Alt+Delete
At the Task Manager window, there should be tabs, click Processes.
Look for firefox.exe under the Image Name column
Click End Process at the bottom
Try opening it again. I had a similar problem with Windows Media Player long ago. I clicked it, but nothing happened. My friend said the computer may think it's still running so when you try to open it, you get no response. I'm not sure if it'll work for FireFox, but it's worth a shot.