On board chargers will "eat" a battery if left unpluged for a period of time and yes they will not charge a dead battery. I would try hooking an amp meter in line on the positive wire to see how much of a draw there is, may be that your charger is bad, but I have seen different brands do the same thing, an old style charger that has switches to go from 10 then 50 amp may bring your battery back, or hook up a small 12 volt light then your charger to get voltage flowing through the battery and see if it will take a charge then. My opnion, I don't and won't own an on-board charger.