I understand your frustration and I'm with you on this. You will need to read above and answer all the questions or I can not help you. I am not there. I'm at my house. I can't see it. It is probably simple once I understand what you have. There are several questions in my last post. Please answer each one. I have not asked you to trouble shoot. I am trying to do it for you.

I am guessing (which I hate to do) that you have a 6V system with a coil that needs no external resistor. I'm guessing the motor may be a car motor with an electric solenoid and a spring loaded V8 ignition switch. I'm guessing the switch, or it's wiring, no longer has a circuit for energizing the coil during crank (far clockwise position of switch). It still does have connection to the coil when switch released ("on"/"run" position of switch). I'm guessing motor is still cranking a little (momentum) when switch released and coil is then fired to start motor sometimes. Arm chair guess: Bad ignition switch, loose wire, broken wire. solenoid "R" circuit.

If the system is 12V now, different guess. Will adjust opinion if and when I get more info. Nice to have Msrs. Lederman and HotRod Jerry's opinion and anyone else.

Right is right, even if everyone is against it, and wrong is wrong, even if everyone is for it. - William Penn