Diagnose this car, Please. [updated]

[Acer]

UPDATE:
Garage still can't get it to start, still pushing to replace the starter.
Garage saying they tried the fuel pump and it worked.
Garage saying it was not showing any codes. Now, this last one simply confuses me because the check engine light had been on for a long time prior to this so there should have been something, even if not related to the present problem. This suggests a battery disconnect, but that would be an entirely different set of symptoms.

It's got rust issues and other old car problems, so my son (it's his car) is very resistant to trying anything more than a few hundred in repairs--especially experimental parts-jockeying.

[mrbigstuff]

Ground cable? Sometimes those develop breaks due to rust. Check all powered connections

[JPK]

My best advice: Check some of the grounding locations. I have found these can be the root cause of most illogical problems.

JPK

[gadje]

You have a code reader, and check engine light was on for a long time.., too bad you didn’t bother to read the code long ago…

[DRR]

August West wrote:

i do remember my triumverate (which will soon be gone), "gas, air, spark"

You forgot compression!

[DRR]

I don't know if you're still following this thread but this seems electrical related. Replacing a starter seems like a red herring. Did they remove the starter and bench test it? If not then they're just turning the key and it doesn't start and saying "it needs a starter first" which is what many shops do because many shops do not actually fix cars they mostly just replace parts.

If you have bad electrical that could also lead to no/weak spark in one/multiple cylinders which would lead to the poor/no acceleration symptom. It could also indicate not enough juice to the starter, which is why they should bench test it. Poor/inconsistent electrical delivery to the computer could also cause the computer to lose power at times, causing the code reset.

My prevailing hypothesis is you have a bad harness/ground somewhere, but troubleshooting that is going to take more time than it's worth to pay. At the very least, 1) Bench test the starter 2) pull the plugs, my guess is they're fouled from misfires in multiple cylinders. If it's just 1 cylinder you might have a shot at fixing it but my guess is it's a deeper problem than just a coil or a plug wire.