2013 Chevy Spark intermittently no starts

I have a 2013 Chevy Spark that was showing symptoms of the starter starting to go bad. You would turn the key on, all the dash light come on, but you go to start the car, and nothing would happen, not even a clicking noise. Tested the battery, battery is good, replaced relay with a new relay and it did the same thing. Replaced the starter and the car continues to do the same thing, intermittently, sometimes it starts, sometimes it doesn't. I was thinking it could be a bad ignition. Is there any other trouble shooting things I should do to figure out this perplexing problem?

If you jump the starter and it starts. Suspect neutral safety switch or ignition switch. Try moving gear selector through the ranges. Try starting in neutral.

I jumped the starter and it engages no problem. I just want to make sure I understand what you are saying, I should try to start the car while it is in gear beginning with neutral? If it's a bad neutral safety switch the car will start?

It should start in neutral.

It should start in neutral.

This. It's a test to see if maybe the car either is fully going into park, or thinks it's not in park. The car should start in nuetral, just like it does in park.