Short to ground is not what I was describing - with extreme resistance - approaching an open circuit - the connection was bad. Not a bad ground, a bad connection. You said in part "If the ground itself was bad, it couldn't be fixed". The chassis is the ground.What you describe to me is a short to ground with a lot of resistance creating a lot of heat. You had bad ground connections, not a bad ground. If the ground itself was bad, it couldn't be fixed with making better ground connections.
True. But not as true as you suggest. These three points are still required in order to start a car. As far as the solenoid control wire (yellow in my experience) is controlled by the computer. Of course the computer also controls some lighting in the vehicle, such as dimming to extinguish interior lighting - I believe the computer controls that. It's possible the computer is going bad. But before I run out and replace the computer I'd check the battery connections at both ends and the solenoid control wire. If those are not the problem then further diagnostics is required.Granted but this is old school. A lot more is tied to the ignition now through the electronics for a vehicle to start.
Same neighbor had a car that wouldn't start. So we jumped the starter and forced the engine to turn over. That didn't work. Not unless he held the key in the start position. As SOON as he let go of the key the engine would shut down. The computer just would't accept an attempt at running the car without the proper key. And the key had a chip (resistor) in it. And that was the entire reason why the car wouldn't start - the cable that made the connection to the key had failed. The solution in that case was to find that cable and bypass it with a resistor of the same value as the key resistor. Once that was bypassed the car could be started at leisure. Probably could have been jumped at the starter with the key in the on position too. But the car - as old as it was - was not a target for thieves. Just goes to show - fully diagnose the problem before you start throwing parts at it. In this case checking and cleaning battery terminals and connections is NEVER a bad idea or starting place.