Ignition mystery

Here is what is happening. I bought the jeep back in February, I needed it to pull a trailer to move and I wanted another 4X4 my last FSJ had died a couple years ago and I wanted another jeep.. The truck had been owned by a young guy who was modifying it, it has been lifted and a few other things changed. It had no radio in it when I bought it. It did have a push button starter but the guy said he had changed it as part of his mod's to make a rock crawler. (I have no idea why that would be so) I had an old radio put in it a few days later. The problem started as just an occasional screech that I thought sounded like a bad bearing. It slowly got worse. It always showed up when the motor was warmed up. It never happened unless the motor was warmed up. it slowly went from the occasional screech to being almost continuous after the engine was warm. finally the starter quit so I replaced it but the problem just continued to get worse. I replaced the module on the steering column but again it didn't work, I replaced the ignition switch but it simply got worse. I even replaced the starter relay module but it just got worse. The last time it happened it wouldn't stop. The starter wouldn't stop turning the motor even if the switch was turned off. I had to disengage the battery to get it to stop. I can hook the battery back up as long as I don't turn the key but turning the keep to any point off or on just starts the engine turning over and I have to unhook that battery to get it to stop. I've been told all kinds of stuff from a short under the dash to a short somewhere under the hood due to it's being associated with the engine warming up. So far nothing has helped and now the jeep just sits in my driveway. Anyone have any ideas about this? I am considering just bypassing the ignition switch and putting another push button on the dash but I don't know how to hook it up. I didn't pay close attention when I removed the old one.

Sounds like either the ignition switch is bad and keeps sending voltage to the starter, or the starter solenoid isn't releasing when you turn off the switch.

I'd replace the ignition switch first (there have been posts about bad ones, do a search) and see if that takes care of the issue. The previous guy put in the push button switch, I'm thinking, because the regular switch was dying.

Is yours an auto or stick? The starter button also helps if you stall on the rocks. It's easier to press a button than turn a key (less risk to breaking key off).

Did this happen before you removed the button switch or only afterwards?

Sounds like either the ignition switch is bad and keeps sending voltage to the starter, or the starter solenoid isn't releasing when you turn off the switch.

I'd replace the ignition switch first (there have been posts about bad ones, do a search) and see if that takes care of the issue. The previous guy put in the push button switch, I'm thinking, because the regular switch was dying.

As i said in my first post I had already replaced the ignition switch, it did indeed turn out to be a bad starter, the solenoid was bad. I installed a push button and that didn't work, the only alternative was a bad starter. I took the starter back to the auto parts store and they gave me another one. It worked perfectly, so far, thanks for your suggestions. It was a synergy of at least two different problems that caused this debacle. I think the ignition switch was the original problem and it led to the starter going bad. I replaced the starter but the problem continued. I then replaced the ignition switch but the starter refused to stop turning, I thought it was the original problem just getting worse so i installed a push button starter only to find the starter still wouldn't stop once turned on. Another new starter solved the problem.