I would have thought the logical thing to do is run a temp lead from the starter motor to inside the car and attach to a multi meter.
Take a note of what a normal start looks like on the multimeter and compare to what it looks like with no start. If the multi-meter is showing same on both then its definitely the solenoid/start motor. If its showing no current in the no start, then you have a electrical issue.
I find it hard to believe a dealer couldn't trace the fault if it is easy enough to get the 3 into a none start situation?
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