I had a similar starting problem with my car when I first got it. The symptoms I experienced were that the starter would not crank even though I seemingly had a full battery load and the car was warm. I could get started with a jump or by topping off the battery with my charger (a battery charger is a DMC owners best friend).
The problem was simply a corroded grounding bolt where the negative side of the battery connects to the frame. This bolt tends to electro-corrode giving a poor ground connection. When you get jump-started, you are supplying power directly between the positive system side and a new ground connection established with the jumper cable and your car starts right up.
DeLorean Owners Association
Regional Chapter 41