This sounds like the large battery negative cable is loose or corroded away. You'll see a second, smaller negative wire from the battery's cable clamp that bolts to the body. That is the ground return for the tail light, head lights, power windows, radio, heater fan, etc. It handles the return current from everything except what's on the engine and transmission.
When the larger negative battery cable has a break in it, current is going to try to find an alternate path back to the battery when you try to engage the starter. That alternate path is through the braided ground strap at the rear of the engine and attaches to the firewall or sometimes the inner fender. That is designed to handle the very light radio interference, not the 200 - 300 amps needed by the starter motor. That's why it's getting hot.
Very often that braided ground strap corrodes off. What you can do is unbolt it from either end, then observe the starter will make no effort to engage. The next step to verify my suspicion is to use a test light or an inexpensive digital voltmeter to look for an excessive "voltage drop". Place one meter probe on the battery's negative cable clamp or bolt. Place the other probe on a paint and rust-free point on the engine. Electrically, those two points are the same, so you should see 0.00 volts all the time. If the cable has a break in it, you'll see the full 12 volts, but that may not show up until you have a helper turn the ignition switch to "crank".
If you're doing this test with a test light, place the ground lead clip or the probe on the battery's negative post and the other one on the engine. Again, since both are in the same place in the circuit, the test light should never light up. If the negative cable has a break in it, the light will light up either dimly or full brightness, when the ignition switch is turned to "crank".
Here's links to some related articles that might be helpful:
https://www.2carpros.com/articles/everything-goes-dead-when-engine-is-cranked
https://www.2carpros.com/articles/how-to-use-a-test-light-circuit-tester
https://www.2carpros.com/articles/how-to-use-a-voltmeter
They're using an "auto-ranging" digital meter in this last article. That's an expensive feature that often isn't needed. If you need help setting up a less-expensive standard meter, I can help with that.
If you see any voltage higher than a few tenths of a volt when trying to crank the engine, the negative cable must be replaced or repaired. Repairs to it are usually not worthwhile. The copper strands corrode away under the insulation where you can't see, at either end. By the time you cut away enough to reach nice shiny copper, the cable is too short to reach the engine.
A bad negative cable can also cause damage inside the vehicle. I ran into one many years ago that melted the throttle cable. Since the engine and transmission were mounted on rubber mounts that insulated it from the body / frame, the only path the starter's return current could find was through the throttle cable, into the body sheet metal, then through the smaller negative battery wire. The throttle cable got so hot it melted the plastic casing. The clue was the accelerator pedal wouldn't move when I tried to press it.
Please let me know if this helps or if you solve the problem.
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Tuesday, June 14th, 2022 AT 6:44 PM