I recently was having troubles with Firefox, I was running Firefox Beta 18 - it started saying it could not update. So after repeat failed attempts, I figured I'd uninstall it and re-install a fresh version. It will download, I can find the file folder, but even when I try to run it as an administrator it won't open the installer. I downloaded three different versions, all do the same. I'm currently running Windows 8 and have had Firefox for over two years on Windows 7. When I upgraded to Windows 8 it transferred seamlessly with no problems. I'd like to be able to use Firefox again.
You can try booting the computer in Safe Mode with Network Support. This can be done by opening msconfig.
Enter Desktop mode by pressing Windows Logo + D
Windows Logo + R
Type msconfig and press Enter
Click on the Boot tab and choose Safe Mode with Network
Then restart your computer and it should automatically enter Safe Mode with Network Support. From there, find your installer and try running it again. When it's done, make sure to go back to msconfig and uncheck Safe Mode.