2004 Chevy Malibu not starting

My car will start fine and then out of
nowhere I will go to start it and
nothing.  The lights and radio comes
on.  The windshield wipers will come
on by themselves and the trunk will
open by itself.  I never know when it
went start.  Then I leave it overnight
and it will start like nothing was wrong.  
The battery is good and have also
checked the alternator.  It is driving me
crazy.  Does anyone know what this
could be? Thank you