We have a Panasonic Genius Prestige 1200 W microwave. The door won't open. Tried unplugging and plugging in; that worked once, but now doesn't help.

Sounds like the door catch is stuck. Perhaps this will help;

Door catches.

One of the latches has broken off and is not lifting the dother latch clear of the housing. Remove from any power source, remove the cover of the cabinet. Slacken off the clamp mechanism and ease the clamp over the guide to allow the door to open. When a new door lever is in place, the door may be easily adjusted by slackening off the screws that clamp the door catch/actuators in place whilst holding the door closed and then tightening the screws. The rear of the door may be adjusted by slackening the lower door hinge screws and adjusting as required.
I hope that helps.