2002 Overland starting problem.
 

Out of nowhere my 2002 overland would not start firday after work.Lights came on inside and out, motor just would not turn over, no clicking or any other sound. Hooked jumper cables to it for a minute or so and it started right up. Had the battery checked and it was fine. Tightened the battery cables and it was ok. Tried to start it this morning and the same thing happened. Moved the shifter back and forth between park and neutral and it started in park. Rest of today it started fine, 6 or 7 times. Can't really have this happening as my wife drives this back and forth from colorado to missouri. I have checked all connections and everything is tight, even threw a new battery in. Could it be a neutral safety switch? I have the 545 rfe so it is called something else and is inside the tranny housing above the valve body.