Chrysler Repair: No starter motor--sometimes, neutral safety switch, solonoid

Question
2001 Chrysler Town & Country- Occasionally won't start ( meaning my wife
will not drive it!)
Like some other threads you've answered.  All the lights go on, no old time
starter motor/solonoid click- almost complete silence  when turn-key, but i
do detect a slight 2 second or so quiet whirrr and then silence.  I brought it to
2 mechanics and it started for them so no diagnosis. One said the computer
showed no problems.  But it still occasionally won't start.  I'll wait a few
minutes or so and then it  does kick over.
Stumped,
 Buzz

Answer
Hi Buzzy,
This will of course be something that you have to catch it "in the act". The quiet whirr is the fuel pump which does indeed run for a couple of seconds but then shuts off if the engine isn't started. The possible no starter causes are: the ignition switch, the starter motor relay, the park/neutral safety switch, the wire from the relay to the starter motor solenoid (which makes the loud click). Begin with park/neutral safety: move the shift lever slightly off the center detent position on either/both sides and hold it there while you try the starter again. If it goes then it is a matter of adjusting that cable/shift rod at the transmission connector.
Then have a helper listen/feel for the starter relay to click when the key is tried again. It is located in the power distribution box near the battery under the hood. If it clicks then the ignition switch and the park/neutral safety switch are ok. If not, then from there it requires a volt meter to verify whether or not the voltage from start position of the ignition switch is reaching the relay and whether the p/n switch points are closing as required. If it does clicks, then you need to verify whether the relay is sending 12v to the starter motor solenoid on the brown wire that connects them.
Those are the basics.
Roland