The "already running" error occurs when firefox was not shut down cleanly. If you look in $HOME/.mozilla/firefox you'll see a directory named something.default. Enter that directory and delete any "lock" and ".parentlock" files you see there:
Replace "abcdefg" with the name of the default directory on your system.
rm -f lock .parentlock
This problem doesn't occur as often as it once did, so Mozilla must have cleaned up some of the code that removes lock files. But it does still happen as you have discovered, and it must cause novice users fits because the reason for the problem is so obscure.
I think rebooting may clean out the locks, but that's not an acceptable solution on *nix systems where rebooting is always the last resort.
Thunderbird can also fall victim to this problem, but it doesn't happen as often with TBird as it does with Firefox.