Chrysler Repair: 1996 Chrysler LHS, neutral safety switch, bells and whistles

Question
I just purchased a 1996 LHS, 3.5 V-6.  I got it home and parked it.  The next day, I went out to start it and when I turned the key, all lights, bells and whistles came on as they should.  When I went to start the car nothing happened.  I can hear the fuel pump initiating and there is a click in an electronic module in the dash and thats it.  I have jumped the starter and it turns over fine.  There is a new battery in it and it is fully charged.  I have cycled the transmission shifter to neutral, suspecting the neutral switch with no luck.  I have unlocked both doors manually thinking it may be the factory alarm with no luck.  Could it be the key switch or key module?

Answer
Hi Darryl,
No I don't think that the key module is involved. But it could be the start position on the ignition switch or the starter relay in the power distribution center. The yellow wire at the ignition switch should carry the 12V (if it is getting thru the switch) to a yellow wire on the relay, also may be labelled as A. I would pull the relay and then with a voltmeter see if you get a 12V response on any pin which otherwise has no voltage at the socket when you try the starter key. If you do, then the ignition switch and yellow wire is o.k. Then you might also put the relay back and listen for that relay to click when you try the start position. If you don't then check that black/light green (C pin) is grounded (which is the one that goes thru the neutral safety switch and to the controller), and if it is then the relay is bad. If it isn't grounded then you need to check the safety switch.  If the relay clicks, then you need to check whether the 12v from the relay points is getting to the starter motor solenoid on the light green wire when you activate the relay via the ignition switch. That is pretty much a check out of the starter motor system, which you already know will work via a jumper. So it has to be one of those components/wires that is not doing its job.
Roland