I'm sorry but there is no way it read 15 volts with the car not running. I work with electrical every day.
As soon as the alternator goes off the voltage starts dropping back closer to 12.4 volts. Hell most charging systems don't even charge above 14.5 volts and the fact it is not charging with the car off says it wasn't at 15 volts.
All that aside you have a definite electrical problem. Even if the terminals look clean take them off and clean them anyway. Check voltage to the starter too.