Engine runs for about 30 seconds and shutdown like an electrical shutdown as opposed to a fuel related shutdown.

Possible bad fuel pump

you have low fuel pressure for some reason, pump may be going or fuel pressure regualtor on fuel rail is bad.

pressure should be 43 psi, key on , engine off. and 34 with engine running.

Try this to confirm low pressure. Turn key to on and listen carefully for the pump to hum for 5 seconds. When it shuts off, turn key off. wait 30 seconds or until you hear relay click under dash. then turm key on for 5 seconds. repeat one more time. Then try to start engine. If it starts right up, pressure was low.

What you did was prime the system and built up pressure before start.

The pump only runs for 5 seconds when you turn key to ON, unless the engine starts. Then it stays on.

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That could be a few things but we need to find out if it is fuel related or electrical related. A quick way to find out if its fuel related is to spray some starter fluid in the breather for 3 seconds. If it starts and go dead it is fuel related. Do this test a couple of times and you should get the same results. It should runs a few seconds and then go dead.. Fuel related issues means fuel pump and filter needs to be changed. and some times fuel pressure valve. Try this first Good Luck!!!

Ok a quick check. When the engine cuts out and you go for restart it dies within 5 seconds. Next time put the ignition at position 2 (on but not starting) and wait one minute, then start the car. If the engine again runs for 30 seconds before cutting off this tells you its is a fuel problem. If the fuel is supplied slowly it fills the carburettor fuel bowls and when the car starts it quickly uses up these local reservoirs of fuel faster than they can be replenished. When you try to restart immediately there is only a tiny amount of fuel and so it used up almost immediately. By leaving the ignition on 2 for while it gives the pump time to fill the carburettor bowls and this takes a while longer to run down when the engine starts. Just before moving on does the car have a choke OK remove the low tension connection to the coil, basically remove any chance of a spark. Put a big old towel around the carb. Now remove the fuel line at the carburettor and put ignition on 2 to engage the starter pump. Listen to pump operation and look at the rate of fuel being pushed from the disconnected fuel pipe. If the flow is slow check on pump and filters.

check the actual fuel line. Also is it fuel injection or carberator

if your engine starts up and dies right away the you probably have a fuel pump problem and the service ride control mean that your air ride compressor has gone bad just turn your key to the on position and wait about 30 seconds you will here buzzing from the left rear wheel area if the compressor is working

1989 Chrysler 2.5 L Turbo has a duel hall effect pick-up in the distributor. It is possible that the pick-up is not working. A "start and stall" indicates that this may be the problem.
Another problem may be the fuel system. Check fuel pressure with key on... should be 40-50 psi on multi-port. 30-40 on TBI
PS If the auto shutdown relay quit then you would not get a start at all. PSS oil pressure will cause a similer problem

Im having the same problem. Here's a question for you, is your cruise control working?

Turn your key on for 10 seconds but do not start the engine. That will give the fuel pump time to built pressure. After the 10 seconds try starting the engine. If it starts right away you may have a weak pump or dirty filter.