I would start over by trashing Firefox and then downloading and installing a fresh copy. Before running the dmg file, make sure to read How to download and install Firefox on Mac for installation details.

P.S It might also be a good idea to completely remove all of your Firefox user data and settings (profiles.ini file and Profiles folder) when you remove the Firefox application from your computer. On OS X 10.7 or above:

1. Click the Finder icon in the dock.
2. On the menu bar, click the Go menu, hold down the option or alt key and select Library. A window will open containing your Library folder.
3. Open the "Application Support" folder
4. Delete the Firefox folder containing profiles.ini and the Profiles folder.

I have tried both of those suggestions and still no luck. The program still wont launch unless I delete all of the user profiles and create a new one. Then if I quit the browser it will not launch again unless I do the same thing.

I did a search and found this thread started by someone with a somewhat similar issue, in case it helps:

https://discussions.apple.com/thread/5088026 Why does 10.8.4 state that I have never opened Firefox???

Okay, well I did that command in terminal and got the response "2435".

I don't know what that response means. Hopefully a Mac user will be along to help but if not, try over at Apple Support.

Hello the above question asked also (and solved) at Apple Support Communities : https://discussions.apple.com/thread/5271892?tstart=0

thank you

Thanks for reporting this, ideato. I'll mark this thread as "solved".