2000 Accord fails to start
 

I just bought this vehicle a few months ago. This happened twice now.
The first time my son left the running lights on by mistake and after
a couple of hours the car was dead. It just did it again but this time
he was listening to the radio on accessory for about 15 minutes and
dead again. I am thinking battery not holding charge. I get no idiot
lights warning of charging system so I assume the alternator is doing
its thing. It starts immediately on jump. Any comments. Thanks