It was a bad hair day for Firefox. Major javascript madness had been run down to something in ~/.mozilla/firefox/, and removing it had solved it. Then a regular fairly basic site failed to display correctly, so I tried removing the <random-string>.default directory to try and leave settings in place.

Bad idea. I got the 'Already running' error, looked it up, checked for lock files where I was told, did an extensive purge of unknown entities and eventually resorted to
su

updatedb
locate lock |grep firefox and got those also.

Now it says Nothing, and exits silently. If I try it in a terminal it gives me MIT-MAGIC-COOKIE-1 keyError: cannot open display 0:0.
echo $DISPLAY returns
:0.0

The box is a new 64 bit HP laptop running 64 bit browser & plugins and is certainly not embarrassed for resources. firefox from Slamd64-12.2 and later 3.0.5 ran here. Short of the 'm$ solution' of delete & reinstall (Which never works in linux anyhow), I am out of ideas. Can I have one please?

Firefox is okay, what you're running into is a X11 thing. I'm guessing you've tried restarting X, or at least rebooting? I'm not sure why it would be just Firefox, but if restarting X doesn't work, you might need to delete some X11 lock files.

Okay. Next day (rebooted) it's now saying

XDM Authorisation key matches an existing client! Google has a lot to say about this, but eventually I ran down an ~/Xauthority and ~/.ICEauthority in another directory. I should explain I have Slamd64 and Fedora, with separate users having separate names in a common /home directory. But of course, I did tweak uid & gid so that each was the same.

That extra .Xauthority must have existed for weeks (As I have not booted Fedora in a while). Why only ff and not seamonkey or anything else noticed it remains a mystery

Thanks for the pointer. FF now boots.