How to check the asd on a 1994 Chrysler Lebaron?

Does the starter crank the engine? If not, look for blown fuse links. Those are the gray, green, orange, black, and white wires going around the left strut tower. If you pull on them and they act like a wire, they're okay. If they act like a rubber band, they're burned open.

If the starter cranks, measure the voltage on either small wire bolted to the back of the alternator with a test light. You should see voltage there for just one second when you turn on the ignition switch. That will prove the automatic shutdown (ASD) relay is okay and the Engine Computer has control of it. You should also hear the hum of the fuel pump for that one second. The voltage at the alternator wires must come back during engine rotation, (cranking or running). You can also measure that voltage at the positive ignition coil wire. You didn't bother to list the engine size. If you have the 3.0L V-6, you can also measure that voltage on the 12 volt feed wire to any injector. The injector on the four cylinder is harder to get to.