reply to TheMG
Re: Furnace starts, then shuts off. I'm gonna say flame sensor. Look at the burner furthest away from the ignitor. My furnace has 3 burners, ignitor on the far right, and the far left has the flame sensor. It's a probe that sticks down into the flame path to sense that the burners all ignited properly.
You can remove it and clean it with some emery cloth. That should bring it back into operating condition to test. If that works you may want to consider replacing it.