strange one

today while turning around in my car park the car suddenly stopped (miss fired to a stop),tried to restart engine turned over fine immobiliser light went out but wouldn't start, checked all fuses and earths under bonnet still nothing for 1/2 hour then started and has been fine ever since but noticed that with lights on or heater etc the interior light was pulsing as did the headlights etc ,i suspect that the alternator is at fault but cant think why it wouldn't start any ideas ???

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