87 corolla issues

I recently bought an 87 Toyota corolla fx 16 as I totaled out my other car hitting a deer when I test drove this car I had no issues on this car it had high miles at 197k but it seemed to purr like a kitten it wasn’t until I started to drive it back and forth to work that I noticed the issue when the car is cold it runs and idles fine a little bit of shift hesitation but figured that might be a dirty transmission filter as the fluid appeared discolored however when the car warms up it shifts fine and begins to cut out and the Rpms dip under 1k every 20-30 seconds. It becomes worse when the car is in gear driving down the road it randomly cuts out and seems to lose power while occasionally backfiring and if I come to a stop and leave it in gear it will die if I don’t feather the throttle just right on takeoff or press it to the floor when I press it to the floor it’s slow on take off and sounds like a mix of backfiring and missing and then suddenly takes off like a bat out of hell once I hit about 20 mph. When it dies the check engine light comes on but as soon as I start it it goes back off. I’ve already changed a bunch of the routine stuff since the car sat for a year such as fuel filter, air filter, plugs, wires, coil, rotor, valve cover gaskets, and replaced nearly all the vaccuum lines trying to figure it out thinking its something simple. Any ideas or suggestions?

Is this a fuel injected one or has a carburetor? I know you can read the check engine codes with creating a short between two of the pins and counting the blinks in the light. I don’t remember the specifics of it though. Google it, check on toyotanation forum and also on Autozone car specific repair guides and see what you come up with.
The CEL code might help.

Fuel injected and I have a a key that goes into the pins as I used it before on my old bonneville but I can’t find the place to put it on this car

There may be two coolant temp sensors. The one that signals the ECM may be not working, so the engine is always getting an enriched mixture, instead of only during warm-up.

Here is how to read your codes.
http://straighttalkautomotive.com/OBD1/toyota-OBD-I.html

Quote; “When it dies the check engine light comes on”

The check engine light will illuminate on all cars when they die.
If you said that the light came on and then a few seconds later it dies…that would mean that there is a problem that the ECM sees.

Yosemite

Is this one of those cars that are prone to distributor problems and need replacement once in a while? Even though the light goes off, the code should still be stored in the computer. Getting the code is the first step.