If you can't make the engine kill by any combination of actions that would normally invoke the safety interlock shutdown (like park brake off WHEN SEAT IS VACANT), then there must be a fault in the kill wire leading to the magneto.
It's possible that this wire has come unplugged from the magneto or has been cut or broken.
I found some schematics online, but I don't know which is correct for yours. Post the serial number of the chassis please so we can be sure of how your machine is configured.

Basically, there is a wire connecting to the magneto which kills the spark whenever the other end of this wire is grounded through a switch. Switches which handle this duty are the ignition key switch and the safety interlock switches.

Most machines will permit the engine to run when the seat is vacant PROVIDED the parking brake is locked down.

Because turning off the key doesn't kill it, try this:
With the transmission in neutral, release the parking brake, next rise up off of the seat. If the engine dies now, you likely have a defective ignition key switch.
If the engine still continues to run, you have a problem in the kill wire circuit itself (kill wire is unplugged from magneto or a wire connector in that circuit has lost continuity somehow).