Engine Stalls

Inspect and test all the following listed below:

Oxygen sensor.
Catalytic converter.
Fuel injectors dirty/sticking.
Mass airflow sensor/Airflow meter.
Throttle position sensor.
Manifold absolute pressure sensor.
EGR Valve
Fuel pressure regulator leaking or defective fuel pump.
False air leakage.
Fuel contamination.
Foul/defective spark plugs.
Open spark plug wires.
Ignition coil/Coil packs defective.
Incorrect ignition timing.
Cap and rotor.

Note:If it doesn't apply disregard

Check for fuel leaks at the injectors. Also, check all fuel lines from the tank to the engine. As far as the engine stalling, have the TCC checked. It sounds like the transmission ins't disengaging.

Try checking the fuel pressure for a start: https://www.2carpros.com/articles/how-to-check-fuel-system-pressure-and-regulator, then let me know so we can continue to troubleshoot

Try a security system reset they shut off fuel and or ignition if it engages. that causes issues like yours. see link.
https://www.2carpros.com/articles/how-to-reset-a-security-system

Also check and test the TPS and MAF sensor

Do you mean it dies when you remove the jumper cables or the battery cables? Do not remove a battery cable while the engine is running or I'll have to come over there and smack you! I already yelled at one person today for doing that.

Leave the jumper cables connected but the assisting car engine turned off. With your engine running, measure the battery voltage with a digital voltmeter. It must be between 13.75 and 14.75 volts. If it is, either your battery is bad or it simply needs time to charge up. A totally dead battery needs about 15 minutes on a charger before it STARTS to take a charge. The acid needs time to become conductive.

Also measure your battery's voltage with the engine off and the jumper cables removed. If it's good and fully-charged, it will measure 12.6 volts. 12.2 volts means it's good but discharged. Charge it at a slow rate for an hour, then remeasure it. If you find it close to 11 volts or less, it has a bad cell and must be replaced.

Be aware a bad battery can cause a voltage regulator to stop working, so you might see a good charging voltage of 13.75 to 14.75 volts while the jumper cables are connected, but then the charging system stops working when the jumper cables are removed.

Next, measure the voltage on the large output terminal on the back of the generator. You must find the same as battery voltage there all the time. If you find it's much higher while the engine is running, as in 15.0 to 18.0 volts, AND it's 0.0 volts with the engine off, look for a blown fuse. Without digging up a wiring diagram, I can only suggest that some cars used fusible link wires and by that time many had switched to using a large fuse bolted into the under-hood fuse box. If that fuse is blown, the likely suspect is the old generator had multiple shorted diodes so it appeared as a dead short.

If you haven't found the cause of the problem by this time, I'll find a wiring diagram and we'll figure out where to look next.