06 PT Cruiser occasionally won't start

I have a 2006 PT Cruiser.  Usually it starts, but sometimes it won't.  It "clicks" when I try to start it, the dash lights come on, but it simply won't start.  If I jump start it, it starts every time.  This doesn't happen all the time, maybe once a week.

I have a NEW BATTERY in it, and it tests out fine.  The Alternator tests out at 15.  Took it to dealer and they came out scratching their heads.  "Could be this, could be that, it's a gamble and is gonna cost ya no matter what you do."  

Thing is, once I get it started it works fine all day.  So what could be causing it to not start in the mornings (regardless of temperature.  Hot, cool, weather doesn't matter).  

Any ideas what might cause this intermittent starting problem when everything on the car checks out fine?