First of all, I'm not convinced anything is wrong with the computer. Second, I'm not sure if computers have to be programmed yet for 2003 models. Yours might just be plug in and go.
I'm kind of in the dark yet, so I'm going to start you with preliminary starter system tests. Check the battery's voltage first. If you need it, here's a guide that will help with reading the voltmeter:
https://www.2carpros.com/articles/how-to-use-a-voltmeter
They're using an expensive meter here with the "auto-ranging" feature. You don't need that. Harbor Freight Tools has a perfectly fine meter for around $7.00. I can help you with setting it up if necessary.
A good, fully-charged battery will read 12.6 volts. If it's closer to 12.2 volts, it's good, but fully-discharged and isn't going to run a starter motor. Use a small portable charger on the lowest setting and charge the battery for two or three hours. If you find it measures around 11 volts or less, it has a shorted cell and must be replaced.
Another indication of a run-down battery is a fast, loud buzzing or ratcheting noise, like a machine gun sound, when you try to crank the engine. That can also be caused by loose or corroded battery cable connections.
This isn't so common any more, but if you get a single, rather loud clunk from the starter motor each time you turn the ignition switch to "crank", that is due to burned or arced-away contacts in the starter solenoid, or a corroded or loose battery cable. A few voltage tests will narrow it down.
If there's a problem in the starter circuit, the head lights, tail and running lights, dash lights, and other accessories such as power windows and radio will still work. If all of those things are dead, we have to back up and test around the battery and fuse boxes.
Assuming everything else works, and just the starter doesn't, remove the starter relay from the under-hood fuse box. It's shown in the second drawing. Even though Chrysler was nice and labeled the terminals in the socket, I'm not going to refer to those just yet. That's to show that except for newer models that stuff a bunch of computer controls in the circuit, the following tests apply to all cars that use a starter relay. You can use your voltmeter again, but for this type of problem, the inexpensive, standard test light can be much more accurate, and faster. Here's a link to an article about using a test light:
https://www.2carpros.com/articles/how-to-use-a-test-light-circuit-tester
The third drawing is an enlarged view of the socket we're after. Ignore terminal 87A. That one is rarely used in any application. GM doesn't even include them on their relays. We're interested in the other four. Start with the test light's ground clip attached to the battery's negative post, or to a clean, paint-free point on the engine. At this point I like to touch the probe to the battery's positive terminal just to verify the ground clip has made a good connection. If the light doesn't light up, wiggle and scratch the ground clip until it does. Now we're ready to test.
When you test at a terminal, be careful to not stick the probe into them real far. Just touch the terminals lightly. Poking the probe into them can spread them, then they might make a poor or intermittent contact in the future. Touch the probe to each of the four terminals. The test light should light up on just one of them indicating 12 volts is there. Now do that again while a helper holds the ignition switch in the "crank" position. Now two should light up, the one you found previously and a second one.
For the last two tests, move the test light's clip lead from the battery's negative post to the positive post. We'll be checking for good ground circuits. Ignore 87A again, and the two terminals where you just found 12 volts. We're only interested in the other two terminals. The test light should light up when you touch the probe to either of them.
One of those tests should have not produced the results I described. Now we can look at the numbers on the socket. They correspond to the numbers in the fourth diagram. I'll work later on expanding it if it's too hard to read.
If 12 volts is missing on terminal # 30, check the large 40-amp maxi-fuse, # 8. I pointed that out in the fifth drawing with a purple arrow, . . . because purple is cool. It's rare to find this one blown except after crash damage.
If 12 volts is missing on terminal # 86 when the ignition switch was held in the "crank" position, check fuse # 31. That's in the Junction Block, inside on the left end of the dash. That's my nifty orange arrow in the 7th drawing. If that fuse is okay, you'll notice there's two tiny holes on top for test points. Use the test light to check for 12 volts on both of them when the ignition switch is in "crank". If it's missing on both of them, we'll have to work back toward the switch.
This doesn't apply here, but for the benefit of others researching this topic, mid '90s Jeeps and some other Chrysler models used an ignition switch that had a cam on the end that could crack, then the lock cylinder wouldn't quite turn the switch far enough to get to the "crank" position. Everything else related to the ignition switch still worked. The dealer's parts department has an inexpensive repair kit for that so you don't have to buy a new lock cylinder and have it keyed to match the door lock cylinders. I can describe that in more detail if necessary.
When testing the two ground circuits, if the test light did not light up when probing terminal # 85, the neutral safety switch is not turned on. It's not uncommon for them to develop bad internal contacts. Shift in and out of "park" a few times, then try cranking when it's in "park" and then in "neutral". If that gets the starter working, the switch is going to get worse over time, so get ready to replace it.
The last terminal is # 87. That circuit has continuity to ground through the starter solenoid. Failure of the solenoid for this part of the test is extremely uncommon. Instead, expect to find the light green wire is not connected to the solenoid.
There's the four tests that apply to starter relays on many brands and models. If you noticed the reference to the "PCM", (Engine Computer), at the bottom left of the fourth diagram, that is not actually part of the starter system. It is shown there because it looks at the state of the neutral safety switch when performing some its operations.
Images (Click to make bigger)
Wednesday, December 30th, 2020 AT 8:51 PM