Well I guess there's just a faint possibility that when the car is on the slope, the drivetrain shifts backwards a couple of millimetres and this changes the tension in the cables of the gearbox, so it thinks it is in 'R' not 'P', leading to a lock-out switch cutting the ignition ??? Or I suppose a similar effect on the electrical cables to the starter motor, although that seems impossibly unlikely.
Maybe the rubber engine mountings could do with renewing, and the cable tension adjusting.
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