If the keys in a 2000 Jaguar XK8 are left in the on position all night is the battery dead or is it the alternator that is the problem?

I would expect that the battery is dead; however, instead of jump starting the car, it is far easier on your car's charging system to place a battery charger on it for about 6 hours then start the car. Otherwise, the alternator tries to charge the dead battery at a wide open rate and it can damage your alternator. Mark