[Airjer_]

All that is left is the ignition switch, PRNDL Switch, or the starter. Next time it does it hold the key in the start position and move the shift lever into neutral. If it fires up I would focus on the PRNDL switch. If nothing happens than it would be handy to have a test light with you to see if your getting power to the starter solenoid (purple wire). If there is power the solenoid is bad. If there is no power than you can work your way back to the PRNDL switch and then to the ignition switch.

Its going to be a pain but eventually you'll get it solved!