Accidentally touched the positive battery post with my wrench starter does not engage

Relays are not going to be damaged by shorting the positive post to ground. (The ASD relay has nothing to do with cranking the engine). First listen next to the starter relay or feel it with your fingers to see if it clicks when a helper turns the ignition switch to "crank". If it does not, start with these tests. The cranking system can be broken down into four circuits, each with a corresponding test point at the starter relay. Find that relay, then unplug the connector so we can take the readings there. You can use a digital voltmeter, but for these tests, a test light is faster and can be more accurate. Before we get to testing, check the terminals to be sure they aren't corroded. When you probe a terminal, be careful to just touch it. If the probe is shoved into a terminal, that one can become spread and make intermittent contact later.

Put the test light's ground clip on the battery's negative post or any paint-free point on the body. Probe the black wire in the connector. You must find 12 volts there all the time. Next, probe the yellow/black wire. You must find 12 volts there when a helper turns the ignition switch to the "crank" position. If you find both of those voltages are missing, there is likely a fuse link wire that is burned open.

If those two voltages are okay, move the test light's ground clip to the battery's positive post, then we will check the two remaining circuits for a good ground. Probe the brown wire first. If the test light is bright, that verifies the starter solenoid wire is okay, and the solenoid itself is probably okay. We will follow up more on that later if necessary. Probe the brown/yellow wire. If the test light does not light up, the neutral safety switch is not turning on. You can try shifting between "neutral" and "park" multiple times, but regardless if that works or not, that switch is the suspect. Let me know what you find with these tests.

What are you doing with the ignition coil? Lets stick to the starter system. I should have thought of this right away. Given that you were working under the dash, that is where you are going to find the cause of the problem, and the lack of 12 volts you found on the yellow/brown wire proves that. The fuse link wire has to be okay since you have 12 volts on the black wire.

The ignition switch is mounted low on the side of the steering column. First verify the connector is fully-seated so all the terminals are making contact. Next, since everything else works, there is a real good chance the switch is simply out-of-adjustment. That is set by loosening the two 5/16"-head screws, then sliding the switch up or down the column.

The only other possibility is two terminals in the connector are blackened from being overheated, but that is not likely to occur to the starter circuit since it is not on long enough to get them that hot. Still, look at the terminals corresponding to the yellow/brown wire, and the red feed wire. If those look like they were hot, and the plastic is melted around them, the switch will have to be replaced and those two terminals replaced individually. I will describe how to do that in the unlikely event it becomes necessary.

Please elaborate on "starter engages but it will not start. It tries but it will not turn over.". If you hear a rather loud single clunk from the starter solenoid each time you cycle the ignition switch to "crank", but the starter motor does not spin the engine, that is a common problem with the little silver Nippendenso starters, and it has an inexpensive fix. Before we get to that, measure the voltage on the large battery cable right on the stud on the starter. You must find 12 volts there all the time. Watch if it disappears when a helper tries to crank the engine. If it drops to 0 volts, there is a bad connection or the wire is corroded off the terminal on one of the battery cables.

If this is related to some card or chip, that is not factory. Chrysler did not have any anti-theft systems in 1989. Your starter circuit is very simple and reliable, so we should be able to figure out how to bypass whatever you have in there now that is preventing the starter from working.