I will guess you have Windows 8 or 8.1 Windows will try to repair itself when it thinks something has gone wrong with the installation. If you are stuck in a loop you might need to resort to your recovery media or a Windows installation disk. If you had Windows 8 and upgraded to Windows 8.1 you will need to install Windows 8 again first as your product key will not work with a direct Windows 8.1 install
It is not the heater core causing the fumes. The heaters work by using hot water from the engine, when the heater core is faulty you will normally get a puddle on the floor inside the car but no fumes. Could there be a hole somewhere in the exhaust?