Not disagreeing with Don but it seems like there must be some starter problem. There's pretty much nothing else in the car that can actually drain a car battery that fast.
For a 50 amp hour battery you would have to draw 200 amps to drain it in 15 minutes. This would melt wires or blow fuses anywhere but the starter power circuit.
How hot are the battery wires getting? I calculate about 15 watts of dissipation, each, but it could be much higher at the terminations if they were done improperly or got oxidized over time. Did you happen to notice anything?
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