Short causes loss of all power

I bought this car new; all original. I have an intermittent problem. Sometimes when I try to start it I get power when I turn the ignition on; however, when I try to crank the engine, all power dies and the key is stuck in the ignition. I can disconnect the battery negative, reconnect it, and normally it will then start. I can also hook up a battery charger or jumper cables to it, then disconnect it, and the vehicle will normally start. Apparently, just supplying more volts seems to jump the short and it will start.
Lately, my tricks of disconnecting the battery is not working. I will get power back, but it shorts again when trying to crank the motor; or it will short out just after I reconnect the negative battery cable.
I took the vehicle to a mechanic. He suspected the body control module (BCM). He told me the BCM has a battery back-up and it should leave a code. Well, he checked and I have no stored codes.
Does anyone have experience with this short? I would hate to pay hundreds of dollars replacing various computers without a good guess of what could be shorting.
Thank you in advance for any advice you can give.
Brian