Start by grabbing your owners manual and look at the wiring diagram near the end
If you have lost yours they are a free download from Toro as is the service manual & parts manual
Usually no shut off is because the kill wire has fallen off the magneto or has been cut / chewed through
So pull off the blower housing and check the white wire that goes to the coil
on = open circuit , so no voltage between it and either terminal on your battery
Off = Ground so no voltage to the ground terminal and battery voltage to the positive terminal
People seem to have a problem wrapping their heads around ground switching
If the wire does go to ground then the coil is faulty and needs replacing .
If the wire is intact but does not go from ground to open to ground when the key goes from off to on to off then the next place to go is the ignition relay
The relay shifts ground from the coil to the starter relay and PTO and is energised every second the engine is running
They can stick & fail
The quick test is to pull the blade switch up then try to crank the engine
If the engine cranks then the relay or relay housing has failed .