Accord has no electrical power

My wife drives a 1997 accord se. 120,000 miles. Recently her car has been experiencing problems with no electrical power. Typically this will occur after she has been driving and she parks, turns off the car. If she puts the key back in the ignition, nothing turns on, radio has no power, obviously car will not start. But if she comes back in 30 minutes or so the problem is gone. She first noticed this problem because the alarm would not work after parking her car. Any suggestions as to where and what to look for?