In case you haven't tried it already it is worth disconnecting both battery terminals and using some emery/carborundum paper to clean all the surfaces. In the past I have had occasions when all was well until starting the engine and the 12v supply disappeared and I couldn't restart the engine. Following on from that the 12v supply was fine for low power items such as ignition but operating just the headlights, which had worked previously, failed in the same way. Strange things happen with battery terminal connections when they build up a thin layer of corrosion. The terminal connections seem to act like a semiconductor current switch in which as soon as the current flowing exceeds a certain value they go high resistance but then recovers when the current drops below that value again. Hope this helps.