I sometimes cannot restart Firefox after having used and closed it. What happens is that somehow FF won't close completely, leaving the process running in the background. The fix is to press Ctrl-Alt-Del, to open the task manager, go to 'processes' tab and see if 'firefox.exe' is listed there. When that is the case, select it and press 'end process'. You will get a warning, choose to end the process anyway. After this I can then open FF again.
I don't know if this will fix your problem, as it happens on startup, but it's worth a try I guess. Otherwise I can only suggest a reinstall. If you do that, try to back up your profile folder before you do!