The fact that you have to push on the shifter to get it to crank sounds like the position switch issue. Basically your vehicle has a switch that is closed when the vehicle is in Park and if this is not closed then the engine will not crank or the key won't release.
However, the not shutting off sounds like a possible second issue.
I would suggest starting with checking the voltage on this switch when in park and go from there. You should have 12 volts on the switch when it is in park. So you are going to want to check what the switch is seeing which means you want to back probe each of the wires at the switch.
https://www.2carpros.com/articles/how-to-check-wiring
I attached the wiring below which will help with this. Also, I attached info on this switch and operation. Please let us know what you find and we can go from there. Thanks
Images (Click to make bigger)
SPONSORED LINKS
Sunday, June 13th, 2021 AT 9:32 AM