I had the EXACT same symptoms on my Ford Ranger. After several hours of trying to diagnose the problem on my own, I gave up and took the vehicle to the dealership. It turned out that the positive battery cable went bad. It was providing enough power to run the accessories and headlights, but not enough to start the truck. I'm not sure if this would cause the same symptoms on a Boxster, but have you check out all the cables to be sure?
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