Is this happening every time you start up your Mac? Are other applications are also unable to run too?

If yes, then your Macintosh HD Drive is probably damaged.

If no, then just try to keep a Copy of your profile folder which is located in: /Users/-your user name-/Library/Application Support/Firefox/Profiles

There you'll see a folder with a code. Copy that somewhere safe. Next time Firefox fails to find your profile, just recopy it (the folder) back to that path.

But, according to your description, it sounds like a Hard Disk failure.

Apple Mac forums would be more useful to you then.

I wish you luck.

Zensa posted a very useful command and it works well to solve this problem ...

http://support.mozilla.com/my/questions/785562

Give it a try and it helps ... although your mac will ask for your admin password ... that made me scare a little. Firefox 4 works fine now on my MacBook pro with OS X 10.6.7

I gave it a try but it didn't work, I guess it's back to the drawing board, thanks for the suggestion.