Microwave won't run

I have a 13-year-old range-top Whirlpool microwave. When I hit start, the run-time starts counting down on the display, but the microwave itself won’t turn on. What might be wrong here? Could it be as simple as something wrong with the door latch, or is it something more? I think the fact that the display thinking that the microwave is running by counting down is a strong clue of something. You’d think if it was the latch, then the display wouldn’t start counting down either. Please advise.