Diagnose this car, Please. [updated]

[Acer]

1. Prior to #2-#5 below, occasional oil light at low RPM, goes off at higher RPM, but no hints of what follows. Engine light has been glowing for some time, not flashing, we think it was an O2 sensor.
2. Abrupt loss of ability to accelerate, though the engine continues to run; needed to pull over it was that bad. Engine light glowing (as it has been) but not flashing.
3. Restarting the engine immediately failed (no response, just the engine light flashed), but after waiting a few moments and the engine started as normal.
4. But after a short drive, loss of acceleration again, pulled over again.
5. Kicker: Managed to pull into a nearby shop last night, but today the garage says it won't start, need to replace the starter before they can proceed to sort out the rest.

20 year old car, only 120K miles. Dodge Caravan.

???

EDIT 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.

[GGD]

Has anyone hooked up a code reader to see what the car is trying to tell you is wrong?

Possible it might be getting into Limp Mode to protect the engine, maybe due to overheating. Flashing engine light might be an indicator that the problem is that severe. But code reader will have the clues.

Ignition coil seems plausible, but a code reader would show misfires on one cylinder to confirm it.

I'd be very suspicious of the diagnosis that it needs a starter as the #1 failure unless they've read out the codes. Just banging on the starter might get it to start

[August West]

Fuel pump failing? Complete guess. I haven't had grease under my nails in 30 years.

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

[flareslow]

Clogged fuel filter?

[Acer]

Yes, the starter thing is suspect, and we put the brakes on the work until we could do more research.

Temp gauge did not light during this.
It had died at right about the point it would have reached full operating temperature, but we were still within 10 miles of home.
The code reading we aren't sure about. We are working from a message, and not from direct speaking with the mechanic, and the information on the codes was not given. We are going to call back in the morning to hear for sure if they could at least read the codes.

[btfc]

Had a 2003 Grand Caravan.

Yes, get the codes.

Throttle/crankshaft position sensors are a common issue on those. As are O2 sensors.

But yes, get the codes.

[GGD]

Everyone that owns an older car should have a code reader that they keep in the car, sooner or later it will be needed. A very basic one is not very expensive. Then google the code and your vehicle to see what caused that same problem for others.

https://www.amazon.com/Autel-MaxiScan-MS...B001LHVOVK

[Acer]

I have a code reader, thanks. We went back to read the codes that evening but the car was behind a locked gate.

[Bill in NC]

Always have your own code reader to pull codes.

Might be a clogged cat which can be replaced with an inexpensive aftermarket model.

[mrbigstuff]

Coil gone bad (possibly multiple)