Engine stalls/not fuel problem

There is a short circuit or short to ground or an intermittent open in whatever it is that is popping and what you touch.
Post a photo and I will see if I can identify it and maybe give you a link to the harness to purchase.
Although, if you want to look up the harness your self, these are two good sources for OEM GM parts.
https://www.tonkinonlineparts.com/
and
https://www.wholesalegmpartsonline.com/

Is this a 3.1 or 3.8 engine?

I think it may be harness #587 here, https://www.wholesalegmpartsonline.com/products/Buick/2003/Century-Custom-4DR/HARNESS-Engine-Wiring/2667840/12578971.html

Split that harness cover open and give me the color of the wires. Maybe I can tell by the wiring diagram.

Of course the dealer is going to mark up the price as much as 100% which is twice as much. I see both summit racing and rockauto has ignition control modules for just over $100.00, even an ACDelco for $142.00 and $175.00. I also see a standard motor product one at rockauto for $54.00, you would save a lot more either purchasing your own and installing it or ask them to install the one you purchase. I see the labor time should be 0.8 hours so even if they charge $100.00 an hour, that is $80.00 labor.
Here are the instructions:
IGNITION CONTROL MODULE > REMOVAL & INSTALLATION (3.1L)
Disconnect all the electrical connectors at the Ignition Control Module (ICM). Note the position of the spark plug wires for installation and disconnect the spark plug wires from the ignition coils. Remove the screws securing the coil assemblies to the ignition control module.
Disconnect the coils from the ignition control module. Remove the fasteners securing the ignition control module assembly to the engine. Remove the coils and the ignition control module from the bracket.
To install, reverse removal procedure. Tighten the ignition coil screws to specification. See TORQUE SPECIFICATIONS. Connect the spark plug wires to the ignition coils. See Figure

No, that is too high, should be 0.8 hours.

The only thing I can think of it getting too much voltage maybe from an over charging by the alternator. Remove the alternator, take it into an auto-parts store and have them bench test it for free.

I think it all depends on if it is the ignition control module again that went bad and if so and if before it failed because it overheated or burnt up. If so, I do not see how the crank sensor would cause that, but I could see too much voltage causing something to overheat and burn up.
I cannot even think of why a bad crank sensor would cause an ignition control module to fail.

Check the ground G111 located at the right side of engine on the ignition control module bracket for being loose. Twist the connection real hard by hand and if it moves any at all, it is too loose.

First just check if it is loose.
If it is not loose, do not worry about it.
There has got to be a code or codes stored in that computer memory, can you have the codes retrieved again? Or tell me the codes you did not mention last time because you said "the car registered some codes one for the purge solenoid" but you never said what the other codes were.