[Schurkey]

Starter gets hot, won't crank the engine, solenoid doesn't even click.

COMMON AS DIRT.

The typical problem is that there's enough corrosion on the wire harness, ignition switch, neutral safety switch, etc. powering the purple (fades to pink with heat, time, and oil contamination) wire connected to the "S" terminal of the starter motor, that it won't transmit enough current to activate the pull-in winding of the starter solenoid. Therefore, no "click" of the shift-fork plunger moving toward the copper disc, and therefore no engine cranking.

It can be made worse by having the guts of the starter hot, and the internal windings have higher resistance and perhaps even some mechanical binding of the armature. But the real issue is the lack of sufficient power to the "S" terminal, which is easily verified with a voltmeter on the "S" terminal when cranking. If there's excessive voltage drop...you've found the issue. The "S" terminal is not easily accessible for connecting the voltmeter leads. Consider getting 3--4--5 feet of primary wire, putting a ring terminal on one end, and bolting it to the "S" terminal on the starter solenoid along with the existing wire. Then you can do your voltage testing at the other end of that new, clean, "diagnostic" wire, up in the engine compartment where it's easily accessible. This can be a temporary installation, removed when you fix the problem...or...IF YOU'RE CAREFUL ABOUT ROUTING AND SECURING THE WIRE so it doesn't ground or get burned by exhaust heat, it can be permanent. Realistically, with a Ford solenoid on the fender, there's no reason to leave that wire in place.

You "could" trace that purple wire backwards through the bulkhead connector, past the neutral safety switch, to the ignition switch, and then back to the battery. Clean every contact, clean every connection, replace all the corroded wire. This is clearly the best solution. It's also a heap of work.

The typical "fix" is to put a "Ford" solenoid on the fender, and use the Ford solenoid to power the starter. The "S" terminal gets power from the bigass battery cable via a short copper link, or short jumper wire. The "S" terminal therefore has all the voltage/current it needs.

The "Ford" solenoid doesn't need as much power as the Delco solenoid, so it works fine even with reduced power due to all the corroded connections in the circuit.

The downside to the "Ford" solenoid is that A. it's ugly, and B. it's not compatible with SOME "Mini starters" such as the Delco PG260.

An upside to the "Ford" solenoid is that it gives you a convenient place under the hood to crank the engine during compression tests and other diagnostic work; and the bigass power cable going to the starter is now only powered when the engine is cranking. (IF your vehicle uses the starter solenoid as a connection for routing power to other devices, you'll have to extend and move those wires to the Ford solenoid.)