Car starts and then immediately stops

The first thing to check would be the fuel pressure. It should be 41 to 47PSI and hold within 5 PSI when shut off.

Do you have a security light on or flashing when you try to start it?
Have you scanned for stored codes?

It definitely has an operational immobilizer system. That cannot be totally eliminated.

The only way you are going to find this problem is you are going to have to determine which function is dropping out at the moment it dies.

All "crank, no start" conditions are approached in the same way. Every engine requires certain functions to be able to run. Some of these functions rely on specific components to work and some components are part of more than one function so it is important to see the whole picture to be able to conclude anything about what may have failed. Also, these functions can only be tested during the failure. Any other time and they will simply test good because the problem is not present at the moment.
If you approach this in any other way, you are merely guessing and that only serves to replace unnecessary parts and wastes money.

Every engine requires spark, fuel and compression to run. That is what we have to look for.

These are the basics that need to be tested and will give us the information required to isolate a cause.

1) Test for spark at the plug end of the wire using a spark tester. If none found, check for power supply on the positive terminal of the coil with the key on.

2) Test for injector pulse using a small bulb called a noid light. If none found, check for power supply at one side of the injector with the key on.

3) Use a fuel pressure gauge to test for correct fuel pressure, also noticing if the pressure holds when key is shut off.

Once you have determined which of these functions has dropped out,
you will know which system is having the problem.

Is this something you are just building or has it been operational in the past with this combination?

You said you have 40 PSI of fuel pressure. The spec for a 94 is 41.0 to 47.0 psi. It will be a little less with the engine running when the regulator gets vacuum, but you should see more than 40 key on.

No, the oil pressure does not shut of anything but you do need to find out if the injectors are being cut off and whether it is the power side or the trigger side that is dropping out.

Now, the oil pressure switch does supply a redundant power supply to the fuel pump along with the fuel pump relay. I did have a car one time that the oil pressure switch was shorting out the fuel pump feed when it built up oil pressure. You can simply disconnect the switch to determine that. Since your pressure is not dropping off, I doubt that.

The bottom line is you need to go back to the series of tests I gave you as they will isolate the problem area.

The relay energizes for two seconds when the key is first turned on and resumes when the computer sees a tachometer signal. Apparently it is retaining for a couple seconds when the tachometer signal drops off. Many GM products do that.

It might be difficult to monitor which function drops off the injector plug in that split second when it dies but that is the only way you are going to get to the bottom of this. Welcome to our world.