Did you update Firefox only, or did you do a full update?
First, it is always recommended to do full updates, not partial ones. Also, I've read in the forums that there was a glitch when FF was first updated to 3.6.2 (something to do with locales, if I understand correctly) but it was corrected later on.
To see if you have any errors, open a console and launch Firefox from there. Post any errors received here.
If launching "firefox" from the console doesn't do anything, try launching "firefox-3.6.2". If this works, then the problem is just that the icon is pointing to the wrong executable; you can just edit the task bar icon properties and correct it.
Hope this helps.