I have a gremlin....

Hey folks, hope you've all been well...apologies for the book you are about to read....I have a bit of an issue that I've not heard of before. My truck is an '08 5.7l with 330,000 kms and the Hewitt bypass kit installed. 2 weeks ago I had a new starter installed.
I left my driveway and drove to my father-in-law's house to grab a ladder, about 4 kms. I pulled into his driveway, swung around the bend by his garage intending to back it up to the door. I push it into neutral on my way up to reverse, and the radio shuts off, truck still running. I continue on to reverse, the radio turns back on, the truck shifts into reverse, and the starter begins to crank. I back up a little until I hear what's going on, put it into park and turn off the key. The starter continues to crank. I pull out the key and pop the hood, all the while the starter is cranking, I disconnect the negative terminal and it stops.
After a few minutes of scratching my head, I reconnected the terminal and tried to start it again. I put the key in, turned it only to accessory and the starter begins to crank all over again. Just to make sure I'm not going nuts, I dissconnect the negative terminal, wait 5 minutes, and try it over only to have the same thing happen: the starter engages on accessory, not start.
At this point I'm a bit peeved because I just dropped 1600 bucks on a starter (on a high kms truck lol) and now 2 weeks later I'm having a starter issue. I disconnect the battery a third time, and have it towed. It doesn't go to the original starter installer (they are 2 weeks out from being able to look at it), instead it goes to different garage who are not so swamped. They take it in after 2 days of it sitting there and can't seem to make the problem happen for them. They spend 2 hours removing and checking the starter, the starter solenoid, all fuses and relays. Nothing wrong. The only thing they swap out is the connector wire from the solenoid to the starter, they had to break it to get the starter out. The previous garage had siliconed the connector onto the starter (20 dollar part).
Just drove it home, no issues.....BUT will it happen again? And if it does, I doubt I'll be in my father-in-law's driveway....lol Anyway, sorry for the novel, but I'm curious if anyone may have insight. It's possible I need a new ignition switch or cylinder with key, but how would that explain the radio turning off when I shifted into neutral ? Any help is great, thanks from Canada

 

I'd check battery condition and all ground connections first.

 

Thank you for your reply, I'm picking up a new battery soon, I have no idea how old this one is....

 

I had My starter replaced 2x. Once by my regular mechanic, then that "failed". Took to dealer. Said bad starter. Replaced again. Issue came back. Friend replaced the connections to solonoid- the connector. That was the problem all along. 3500$ down the drain. Caused all kinds of electrical issues.