My AM car radio has tons of static when the engine is running. The
thing is useless when the car is on or even if the key is turned to the
on position right before you start the car. It's fine if you turn the
key to the aux position.

Another clue...

When I turn an electrical motor in the car on and off, it sometimes
reduces the static level...but never eliminates it. And then when I've
fiddled with something and reduced the static, I'll hit the brakes, and
the brake light will trigger the static onslaught again.

I have taken the radio out, and checked the antenna connection as well
as used jumper cables to ground the grounding bolt. No significant
improvement.

Thoughts?