Craftsman starter issue

I have a craftsman 19.5 hp twin cylinder and having really strange starter issues. Initially I could start the tractor with the key but the starter kept running with the gear disengaged. The only way I could stop the starter was to disconnect the battery. I was checking the key switch to see if it was defective. I removed the switch and hit the dash, the mower started and was in gear ( should have had a video of me chasing the mower). I got on the mower, hit the brake and reinstalled the switch and turned off the engine with the switch. Tried to start again and it would not start or even turn over. I charged the battery again and the mower started but started kept running. Bottom line, I have checked the switch for continuity and all is ok, I have tested all the lockout switches and all is ok, I replaced the solenoid but every time I attach the battery cable the starter engages and starts the engine, this happens with the switch installed or unplugged. The engine will start and run, I have to install the switch to turn off the engine. Any ideas would be appreciated.