J-Rooster
If you haven't yet, remove the cables from the battery and clean underneath and inside the clamps. Corrosion can build up between the clamp and post that is not visible with the cable attached. The corrosion can cause some intermittent and interesting problems.
When I read your post this was the first thing I thought of
Once running, the engine is self supporting, but at idle the alternator does not put out full current and any load that exceeds the idle output can cause the engine to die. The battery generally acts as a buffer but if it was low / dead / or had too much resistance due to corrosion it can't. I test drove a car with electric assisted steering once. It had a dead battery and had to be jumped. During the drive I slowed down and let off the gas making a right turn and the car stalled. The electric assist steering exceeded the alternator output at idle and there was no battery to back it up, so the engine died. A slide motor could be a big enough load if the connection to the battery was poor. .
With my small car, I got an intermittent no start condition. When I turned the key to on the lights would come on, but as soon as I tried to start it, boom everything would go out. Resetting the key would cause the dash to light again, and SOMETIMES it would start. Had the exact same symptoms and problem with my dad's car. Cleaning the inside of the clamps solved the problem.
I have also experienced a loose main ground wire cause similar issues.
Good luck, hope you have solve your problem!