Here again, you should start a new question specific to your vehicle. Unlike other sites where anyone can chime in to confuse the issue, here this becomes a private conversation with one or two people sticking with you until the problem is solved. As such, none of the other experts are going to see your addition or have a chance to reply. That may not get you the help you need.
Here's where to start a new question, if you need to:
https://www.2carpros.com/questions/new
Please be sure to list the engine size and mileage. We need the engine size to look up the correct diagrams, and we use the mileage when making generalizations as to the best suspects.
This original question is a year old. In that time, one thing that has become more-known is an intermittent transmission range sensor, formerly known as the neutral safety switch. One potential clue is the starter will work after shifting between gears a few times. The best way to identify this is if you can catch it when it's acting up, and you have a scanner connected to read live data. Under the "Transmission" menu, look at "gear selected" to see which gear is indicted. If it is not "park" or "neutral", the Engine Computer will not allow the starter relay to engage.
Another test would be to remove the starter relay, pop its cover off, reinsert it that way, then press down on the movable contact to engage the starter. (Be sure the transmission is in "park", but the ignition switch doesn't have to be on to do this. If the starter still doesn't engage, we'll need to look in circuits other than the neutral safety switch / range sensor. You'll need a test light and a helper to turn the ignition switch.
Saturday, June 27th, 2020 AT 11:01 PM