Starts then stalls

Could be a bad converter as well. It could be totally clogged causing this issue

Roy

Starter would not make it stall.

First, get the battery and alternator tested. They are the first in your series of checks.

Roy

Still need to have the battery and alt tested no matter how old it is.

Does the starter turn over the motor or click

Roy

Ok, start with basic checks. Fuel pressure, compression and spark.

Roy

Sounds like a door switch/latch problem.

The dead battery has resulted in the engine computer losings its memory and this is affecting the idle control causing the stalling.

Repeated cranking with a half-charged battery can cause the starter to fail to work. I would sugggest getting the battery fully charged, which requires quite some charging time if it is the non-maintenance type and has been drained.

The computer needs to relearn after power is restored and it takes some time too and with the battery charge in poor condition, it would be more difficult to get it to run correctly. Cleaning the throttle body and IAC would help speed up things.

Hard to say. What do you mean by door light?

Did you check the hood switch?
TRy disconnecting the other 2 switches to see if probem goes away.

There sulc be a short in the switch wirings causing the light to be on all the time.

What do you have for fuel pressure

This the page that shows how to check fuel pump and fuel pressure

https://www.2carpros.com/articles/how-to-check-fuel-system-pressure-and-regulator

as if it a sensor or switch need to check for codes
this is one way of RETRIEVING TROUBLE CODES

CAUTION:DO NOT enter self-diagnostic system until all basic engine checks (engine, fuel and spark) have been performed.

Verify CHECK ENGINE light circuit is operational.
Ensure battery voltage is above 11 volts and charging system is okay.
Engine must be at normal operating temperature.
Transmission/transaxle must be in Neutral or Park. Air conditioner and other accessories must be off.
Throttle valve must be closed (throttle position idle contacts closed).
Turn ignition switch to ON position with engine off.
Place jumper wire across "TE1" (or "T") and "E1" terminals in engine check connector. See Fig. below.

Count number of flashes from CHECK ENGINE light.
If system is operating properly (with no codes), CHECK ENGINE light will blink continuously and evenly.

NOTE:If CHECK ENGINE light stays on and will not blink codes, verify battery voltage is present at "TE1" (or "T") with key on and engine off. Ensure "E1" has continuity to ground or self-diagnostics will not work. If ground ("E1") is open, jumper "TE1" (or "T") to battery ground.

A trouble code will be identified by a .5 second flash on and off for the first number. A 1.5 second pause will occur followed by the second number.
If more than one code is stored, a 2.5 second pause will occur before second code is flashed. Once all codes have been displayed, a 4.5 second pause will occur and code(s) will repeat.
Trouble codes are given from smallest number code to largest number code. After codes are retrieved, remove jumper wire to exit diagnostic mode.