With the belt issue, could you alternator not have been charging the battery? In electronic ignition cars, I've seen where there is enough battery to turn the engine over but not enough to operate the ignition. Throw and booster on and it fires right up. Be sure the battery terminals and all grounds are clean.
I was only a mile from home at the time I took the alternator in to be tested it tested good I then put in a new battery and that shows 12.9 volts this was all done after the ride.