So it started once, died, and wouldn't restart? First place to look is the alternator and voltage regulator. If the alternator didn't provide power, then the whole time it was idling it would have been drawing from the battery, which also wasn't recharged after the engine started. Once the battery ran down, the engine died, along with the other electrical users.
Just a guess, but it seems to fit the symptoms you described.
Engineering: Finding complex solutions to simple problems you didn't even know you had.