I've had enough experience of rotten old cars (and most light aeroplanes are electrically simpler than them) to know that if there was enough urge in the battery to start the engine, there wasn't that much wrong with it and if you started to conserve electricity as soon as the "low volt" light went on you should be OK fo some time.
I can only assume that the departing belt took an important cable with it .. or dead shorted one.
