I saw a post on here that was very old but what it said was the batteries would drain and not start unless the block heater was plugged in. I'm having the same issue except it never did this before until we replaced the radiator just a few weeks ago. The weather was the same before and after so it's not colder out after replacing The batteries and alternator test fine and I know there is no connection between plugging in and battery charging. If it's not plugged in they drain very quickly and a jump start works immediately when it's plugged in it starts without any issues. The only thing we can figure is a short of some sort but everything looks ok. If anyone has any ideas on locating the problem or where the short might be I would be very appreciative we are at a loss.