Q: Why did my car start after acting like the battery was dead and how long should I leave it running

Leaving the engine off with the radio and heater running uses accessory power which drains the battery. When the engine is not running, the alternator is not charging the battery. As a result, when you went to start the car, the battery may have been drained substantially depending on how long the key was left on.

As you may know, the alternator is responsible for charging the battery while the engine runs by generating amperage and recharging the battery while the engine turns the alternator. The voltage regulator is a unit that regulates the charging of the battery by the alternator and maintaining a certain amperage while the engine runs. When the alternator is not working properly, this may result in the battery quickly losing charge and the car losing all power as you have described. I would recommend having an expert from YourMechanic come to your location to diagnose and repair your charging system.