Hi Dave,

Given you've replaced the battery cables, the battery, and verified the battery is charged up and still experience the no-crank, logic tells us there's only one thing left; the starter.

But getting it to crank with the jumper cables attached to the outside of the cables' battery terminals, tells us the terminals are loose or the battery is discharged or loose/broken inside. Lots of fuzz growing around the terminals adds to that suspicion.

Also, having no lamp test on the parking brake, brake failure, and bulb-out warning while the oil light glows points at the exciter wire (you substituted), or the alternator's regulator and ground wire. Your mechanic will certainly find the trouble if you can only get it to occur.

Here's how you can chase it down. Prepare a remote starter switch (you can buy one, I'm sure) to connect between the starter test terminal at the firewall and battery +. Next time it happens, have this and your multimeter or test light handy to see where the battery voltage drop occurs while attempting to crank. Start at the battery posts themselves, and suspect each connection (metallic junction) in the circuit from the positive lead post itself, through the starter, and back to the negative lead post. If it suddenly comes to life while testing, think what you might have moved. If the voltage drops across the posts themselves, you're back to a discharged or defective battery, and must again consider the alternator problem.
--
Art Benstein near Baltimore

It's always darkest before dawn. So if you're going to steal your neighbor's newspaper, that's the time to do it.