Chrysler Repair: Sebring wont start, neutral safety switch, starter solenoid


Question
I just bought (yesterday in fact!) a 2002 Sebring Convertible Limited. Started up fine, worked fine all day yesterday. Today it wouldn't start. Then after a while it started up (there is no noise when it wouldn't start) , but after running it I turned it off and went to start it again and it was 'dead' (battery power was ok - radio, lights)... i had the mechanic check it out before I bought it and all was fine.  

Answer
Hi Judy,
This is not unusual, it just takes a little bit of sleuthing to find out what is wrong.
To fire up the starter motor, you need to have both the primary circuit consisting of the ignition switch, park/neutral safety switch on the transmission and the starter relay located in the power distribution center (a rectangular box next to the battery with a removable lid, inside of which you'll find fuses and relays) AND you need the main power from the battery to reach the starter solenoid that is located on the starter motor behind the engine (but that big red cable is probably o.k. because the failure (as you describe it) seems to say that the solenoid is not getting the go ahead from the relay (i.e., you don't hear a loud click coming from the solenoid)).
There are several components in the primary to consider:
1. The ignition switch (it may have a flakey contact)
2. The park/neutral safety switch on the trans (it may be flakey, or be out of adjustment, so try moving the shift lever a little bit one way or the other while in park and you have the key turned to "start" to see if that solves the problem).
3. The starter relay (the next time the starter fails, ask a helper to operate the ignition key while you get under the hood, open the power box and listen for a soft click to come from one of the relays when the helper operates the ignition key to "start"); if you hear that then you know the ignition switch and the relay coil and the safety switch are o.k.; and the problem is either the relay's internal switch contacts, the brown wire from the relay to the solenoid, or the starter solenoid itself. If you don't hear a soft click, then either the ignition switch, the safety switch, or the relay's coil is bad.   
If you hear the relay's soft click, then you have to determine if the contacts in the relay are worn, the brown wire from the relay to the starter solenoid is loose/corroded, or that the starter solenoid itself is flakey. The relay is pretty cheap, and the brown wire can be checked at the solenoid, so you might try checking the wire at the solenoid and if that is o.k. buy a new relay. If that doesn't fix it, then the solenoid on the starter motor is probably worn enough to be flakey.
Unfortunately, there is no simple answer, but if you have a voltmeter or a simple 12V neon glow light probe and you can get the start function to "fail" predictably, I can tell you where to check for voltage to figure out which of the components in this chain is the weak link. I can't be sure which would be most likely to intermittantly fail. If it only will fail for one try of the ignition switch it makes it difficult to troubleshoot because you don't know when it is going to fail and you have to set up your meter before you even give it a try to start it. So you may have to wait till it becomes a bit more intractable.
Feel free to write back if something here doesn't make sense to you. And you might want to buy a neon glow type of 12volt tester at an auto parts store so you will be ready the next time this happens to figure out which components or wires is causing the problem.
Roland