First, roll back IE via the guide given by Buteman through uninstalling the update. Make sure you have a working browser (IE8). In programs and features uninstall Mozilla then reboot. Reinstall; click here
Have you tried uninstalling Firefox using Revo-uninstaller (free version) from click here. It removes all firefox entries in the PCs registry as well as the normal uninstall that Windows carries out. It is certainly worth a try.