Chrysler Repair: 08 300 V6: starter intermittent

Question
I'm having a start problem with my 300.  Sometimes it will just not crank.  all electronics work but no clicking like the starter is trying to turn over.  Then, after several tries and minutes, it will crank fine.  Changed the battery after it started and problem still occurs.  Also tried changing the fob battery, still happens.

Answer
Hi Jeff,
The starter motor is activated by the starter relay. For the starter relay to be activated the gear shift lever has to be in Park or Neutral and it may be the case that its safety switch is slightly off-center from those detent positions. So try moving the lever slightly off the detent on either side to see if that corrects this.
The other item to check when it won't crank would be the starter motor relay which is located in the power distribution box in the engine compartment. Look for it by means of a label on the box itself. In any case, have a helper try key to activate the starter while you listen for whether there is a click sound that comes from the relay or not. Based upon that answer we can then consider what the possibilities are for this intermittency. Tell me whether you have a volt meter if some tests have to be done.
Please read the PS (below) and respond to it.
Thanks for doing that.
Roland