You will have to look at your owner'* manual, to see which Security system is used for your car....

Passkey I and II, use a black pellet resistor on the ignition key.....PassKey III has a transponder in the head of the key, and has PK3 stamped on the key near the top of the shaft of the key....

If it has PassLock, then that is just a blank key with no markings....

The difference between PassKey and PassLock is this: With PassKey I, II, or III, when you turn the key to on, the SECURITY/THEFT light will come on for 3-5 seconds, and then go out....with PassLock, with the key in the on position, the SECURITY/THEFT light stays on......it will not go out until the car starts.....if the car cranks, starts, and then dies after a few seconds, that light will stay on or flash....

If you are getting 12 volts at the purple wire, with the key in the crank position, and chassis ground is ok, and the other connections are ok at the starter, then you have a bad starter(you said you already replaced the starter)....I hope you tested the purple wire with a test light......using a voltmeter is not foolproof....it only measures potential, not working voltage......for example, if you were getting a Full 12 volts on that purple wire, you should at least hear the solenoid click......and if it clicks, and is getting the full 12 volts, then you need a starter/solenoid....

Whenever you test circuits, with low current, use a voltmeter......a circuit that uses high current, such as starters, motors, solenoids, etc., use a test light....it should be the same brightness(12V), as when you put the test light across a fully charged battery.....for example, when you use a voltmeter, there is little current flow, because of the high impedance/resistance of the meter, usually 10M-ohms, or 10,000,000 ohms......but a test lamp has very low resistance, resulting in a much higher current flow........so if there is a voltage drop in the circuit, the voltmeter, because of negligible current will drop all it'* voltage across the 10 Mohms of the meter, making it show 12 volts......but a test light will allow high current to flow...if there is a voltage drop in the circuit, that drop could be much higher than the voltage drop across the test light itself, and thus the light will be dim, even though a voltmeter previously would show 12 volts.....

Okay good news on the revolutions. Seems to likely rule out a cylinder filled with coolant.

Good news! I think I've found the answer on the ignition anti-theft system. Per the owner'* manual page 74 the ignition anti-theft system is the "Take Your Ignition Key With You" system:

"If you walk away from your vehicle with the keys inside, it’* an easy target for joy riders or professional thieves -- so don’t do it. When you park your Buick and open the driver’* door, you’ll hear a chime reminding you to remove your key from the ignition and take it with you. Always do this. Your steering wheel will be locked, and so will your ignition and transaxle. And remember to lock the doors."

. . . and . . .

"If you park in a lot where someone will be watching your vehicle, it’* best to lock it up and take your keys. But what if you have to leave your ignition key? What if you have to leave something valuable in your vehicle?
- Put your valuables in a storage area, like your trunk or glove box, or rear storage area in the wagon.
- Lock the glove box.
- Lock all the doors except the driver’*.
- Then take the door key with you. "

. . . and the pictures show just normal plain old square and oval metal no-frills keys.

Have you physically checked every inch of the fat positive and negative cables from the battery to all destinations? Was the starter solenoid replaced at the same time?

Found a PDF of the owner'* manual online......apparently, the 1994 year did not have a Security system, thus, no SECURITY/THEFT light, and it just uses regular blank keys.....

Sounding more and more like a bad starter, if battery and connections are ok....

I got the car to start!

I used a jumper cable to run a new ground from the battery negative terminal to a bolt on the body of the starter. That seemed to fix the problem. I guess that the larger ground cable that'* in the car now was bad. I should be able to effect a permanent fix by either replacing the current ground cable or adding a second one.

Thanks to everyone who helped!