Dodge Repair: 05 Neon: Intermittent starter problem, neutral safety switch, starter solenoid

Question
QUESTION: 2005 neon SXT no crank problem. Very intermittent most prevalent in the morning and after sitting for a while. Can turn the key a dozen times with nothing happening and then all of a sudden it cranks over and starts right up runs no problem.after it starts the first time it would have no problem maybe for days. New battery, voltage checks good.No check engine light or codes,runs great when it starts. The things I've done trying to track down this problem i.e. jump starter at solenoid it cranks no problem does not change the problem with the key, this kind of indicates the starter is probably okay. If the ignition switch is on and engine is not turning over if I jump the starter solenoid it cranks over but will not start. Kind of indicating to me the same circuit that operates the starter also operates the fuel injection system for starting. I have cleaned and re-crimped as many grounds that I could find in the engine compartment i.e. main negative battery to starter bolt from there to bottom of battery box. Ground from battery to fender well, both left and right grounds to the radiator support. Positive battery terminal to fuse box and also to starter. Of course both battery terminals themselves. Swapped out starter relay,checked fuses inside and out. Check neutral safety switch, switching from part to neutral has no effect and the plug was clean and dry. Checked the harness directly above battery that has starter solenoid wire again the plug is clean and dry. Disassembled ignition switch cleaned and re-grease contacts again no joy. Of course the problem being so intermittent after doing a few things it will decide to start starting LOL
The harness on the backside of the engine feeding the alternator and oxygen sensor shows signs of some heat damage from the exhaust system but I don't think that's where the problem is either.I have pulled the PCM and checked the harnesses and plugs,all clean and look ok. Does anyone know where the PCM gets its ground from?
I have read as many of the comments I could find online and tried just about everything. And I see this is a common problem as far as the intermittent part people taking their cars in and having them check out.The problem goes away for a while and comes back just the same. Sorry to be so long-winded just trying to be thorough thank you for any comments and please any help.

ANSWER: Hi Jeff,
Thanks for all the details about your search for the cause of the starter no crank. I would believe that the best way to find the reason would be to have a volt-ohm meter at the ready to check out the circuit in the failed condition.
My suspicion would be that the starter relay is not being activated to close. So begin by having a helper try the key while you listen for the click. If it clicks but doesn't crank then it has to be the relay points or the brown wire from the relay to the starter motor solenoid.
If it doesn't click then it has to be the wire from the ignition switch to the relay coil/pcm or the wire back from the pcm to the relay coil's other end (a grounding 'action' to activate the points of the relay). The pcm is thus involved doubly in that activation process (knowing when you have closed the ignition switch to the start position and second to ground the other end of the starter relay actuation coil).
If you don't have the wiring diagrams I can attach them to an email I would send to you directly. Tell me your email address but don't use the @ symbol, rather use "at" otherwise the address will be erased.
Also tell me which engine you have, and which type of transmission is in it.
Please 'rate' my answer (See below).
Thanks,
Roland

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QUESTION: e-mail  audio465atyahoo.com
the motor is the small, 2.0. Automatic transmission. I do have a fluke VOM meter. I have some wiring diagrams, they're not very complete. I would appreciate ones you do have thank you. From what I can tell I get no clicking action from the relay, I have swapped relays around to no avail. The problem being so intermittent it's hard to check for power and ground but I am attempting to check those circuits during the failed state.

Answer
Hi Jeff,
I would look at the park/neutral/back-up switch and its wiring as the possible cause of your problem. I will send you all the wiring diagrams and also the instruction from the transmission section about testing it. It is wired to the fuse 7 (for the back-up lamp current) and also to the pcm which seeks a grounding of pin 76 when in P/N. It is located on the left side of the transmission facing the front of the car.
Thanks for the rating/nomination which you are entitled to repeat if you so choose.
Roland