Car running on three cylinders with good spark.

I may be.
get it fixed or
do the tests.
tune it up?
then check spark and compression cylinders and if flooding or not.

Try changing the coil pack

Probably the ECM. Lot's of checks to make to see if that is it. Does it try to fire up if ether is squirted in the intake? Is the security light on? Does the dash say "No Bus" Does the fuel pump come on?

If it has a security system don't bother with a junk yard ECM, the car will kill it. Run for 4 seconds and die.

Place in south Florida specializes in Dodge Reman ECM's guaranteed to work with the security system.

to check miss fire run engine when warm and at idle remove injector wire one at a time when disconnected engine will run rougher if there is no change to engine when injector is disconnected that cylinder is not firing check wire and plug if ok compression test cyl

Actually i doubt the switch is in default here. Especially that if i'm not mistaken the theft light on those was only on the monsoon radio systems and only tells the status of the theft lock on the radio. And if the theft lock light on the radio comes on it's because it thinks it's being unplugged. Taking that in account and reading all the problem you have with the car, i'm strongly leaning toward a grounding problem. So check the negative post on the battery to be sure its not moving or broken in any way, and verify all the grounding wire and straps and replace them if needed. Not many people know this but the ground wires on a car are 100 times more important than the positive wires. Without the grounds, the current has nowhere to go on any components, so that means even the spark plugs stop sparking. If all the grounds are good, just check the battery itself and the alternator just to be sure they are not causing these problems. And if all else fails, then it would be option to change the ignition switch/cylinder. Pretty sure though that you can find one in a scrap yard for less than 150$, those cavaliers are practically raining everywhere in the scrap yards, and you can also use one from a pontiac sunfire which is the same car. Also, you can use most switches from other GMs in the same years, like a grand am, grand prix, lumina, etc. Just make sure that the car you take it from has basically the same equipment more or less than your cavalier so that the zenith has the same number of wires as yours and same positions also.

Have you made sure your getting spark on every cylinder from the coil pack?

This car has seporate coil packs for each cylinder, have you tried swapping the front bad one with a good one to see if they switch ?
The engine you just put in may have come with some blown coils.
Hope this helps
Sam

Most likely needs new coil pack for cyls 3 & 4.They fire together.

Question:
Did you replace the ignition switch or the KEY AND CYLINDER?

These are the only 2 things that can make your engine turn off when you release the ignition switch after starting the engine.

I hope this helps you.
ramonalees.com

ignition mod. grounds,pcm or timing belt could all be it but, I would have to look at timing first.