One common problem with over the range microwaves is that they seem to function normally, lights on, turntable spinning, but they do not heat. Often the issue lies in one or more of the three microswitches not being struck properly by the latch mechanism on the door.

When I run into this problem I usually replace the latch plate, a plastic framework that holds the microswitches, and the three microswitches. Note: there are typically three switches, two of which are NO (normally open) and one is NC (normally closed).