Car starts without key!

Just something to check is there still 2 wires running to the starter. You said the previous owner put a push button start in it. On circle track cars we run a copper strip from the bug lug to the small lug on the starter, then run the big cable to one side of a Ford starter solenoid, then a wire from a push button activates the solenoid sending power to the starter. Don't think this mod would work with a Chrysler solenoid, but it is worth a check.

I followed the two wires coming from their push button and they were both going to the relay, don't remember exactly remember where. (Wasn't going to reuse so didn't care) The only wire I saw out of place was the yellow wire, it was disconnected. So naturally I hooked it back up where it was supposed to go on the relay. When I hooked the battery up, I found that the starter activated. It stops when the yellow wire is disconnected. I ordered a new sign switch, should be here tomorrow.