I've been using Firefox for about three years now, and your problem is ringing a faint bell regarding this problem when I first stated using it.
Try this:
Set a RESTORE point on your system (in case you bugger things up and need to RESTORE to your current set up).
Use Regedit, or Registry Crawler, or some other Registry tool to find all references to "IEXPLORE.EXE". Delete them all. Reboot.
You will still be able to load Internet Explorer should you wish to, but all reference to it as a background task, etcetera, will be erased.
If this buggers up your system (which it shouldn't), RESTORE to the previous saved point - nothing lost but a few minutes of your time.
Good luck - as I said, I dimly recall similar problems when I first stated using Firefox - those problems no longer exist.