I realize that it is obvious, but just want to make sure: a microwave (and GE Profile specifically) won't start if the door is ajar. Just in case you haven't done so: check if there's anything blocking the latch and/or preventing the door from closing completely. GE lists a power surge as one of potential reasons for the oven not starting. It never happened to me before but the solution they propose is to unplug the oven and plug it back in. It may be more convenient to just flip the breaker to the oven, depending on how it was installed. The idea is to reset the controller which may have gone haywire after a power surge.
If none of that works, post more about what's going on, including the actual model number of the microwave oven. Be sure to mention any sounds, lights or display messages you've observed.