I just had a problem with Firefox 26 (which was upgraded in the last few days) on Ubuntu 12.04 64 bit. Not the same as yours though and you did not say what version of FF.
In my case I went to start firefox which I had run last night AND exited normally but Ubuntu said it was already running and I would need to exit that first before running another (weird huh?). There did not appear to be one on any workspace and the Unity launcher was not indicating one. Normally, even if there was one, there would be a pip showing on the launcher and clicking on it would just take me to the open application.
However, ps showed a firefox process running so I killed it and the Firefox could be opened and seems to run normally. Makes me wonder is there is some memory leak causing these problems. Not like they don't have some history of leaks.