Hi Dan. I mostly agree with you. Mostly.
The troubleshooting steps as reported suggest a voltage drop getting to the starter. A booster masks that, somewhat, and gives enough kick to turn things over (and as stated above, it'd be good to know where that was connected). New battery did not help (again, suggesting voltage drop/high resistance). OP says they cleaned the grounds, sort-of ruling that out. I could fault the starter, but since a booster allowed it to turn over, that suggests the starter isn't totally bad. This leaves the cables, which may or may not be the original aluminum.
In Post #10 Doug Reid asked an important question that hasn't been answered: Where was the system boosted? At the battery? At the starter solenoid? Or at an external power socket? The external socket and starter solenoid both bypass a whole bunch of possibilities, including the master contactor. One needs to know the circuit diagram and where the boost was connected to intelligently diagnose anything.
Of all the subjects a mechanic studies and needs to know, electrical theory is easily the weakest for most. When it comes to owners, the same thing applies. That's why we see suggestions to replace this or that "because that's what my problem was" or something. The circuitry here is a lot more complex than that, and without understanding it, and the effects of tiny resistances, all suggestions are useless.
Ohm's Law: E = I x R. Voltage equals current times resistance. We have a starter that can draw as many as 250 amperes. We might have a bad contactor or cable that presents a resistance of 0.05 ohms, a figure your typical multimeter will never measure accurately. Its test leads might even have that much resistance. But that 0.05 ohms times 250 amps equals a 12.5 volt drop. In a 12-volt system, that means you get nothing at all. And that's with one-twentieth of an ohm. Of course, the resistance causes a massive voltage drop, which reduces the amperage, which also reduces the voltage drop, and you can see that it gets a bit complex. In any case, measuring the voltage across suspect components is the way to find the fault. If you turn the master on, and connect the multimeter (set to volts) across the starter contactor, you will see 12 volts. Battery voltage. This is because the meter is drawing a tiny bit of current to get its reading, and it is grounding through the starter. That doesn't make much difference to the microamps drawn by the meter, so we get an accurate reading. Now you hit the starter, and the voltage should drop all the way to zero as the contacts short the multimeter. If the voltage drops to one or two volts, you have a bad contactor. Across the master contactor you should see zero volts when the master is on, engine not cranking. Crank it and see if the voltage rises above zero. If it does, the contactor is bad. It has resistance that diverts a few microamps into the voltmeter.
These small voltages add up throughout the system, since they're all in series. You might replace a cable and get rid of a two-volt drop, but there are a bunch of other resistances in that circuit that are giving a total of three volts drop, and the starter's performance is still not so good. You've got to find them all. If you don't, one or more will just get worse and strand you somewhere someday, a situation that instantly gets a lot more expensive than just doing the job right in the first place.
