Have there been any incidents caused by an inability to shut down an engine?
Qantas Flight 32
Enroute to Sydney, Engine Number 2 of the A380 disintegrated explosively. The shrapnel of the explosion destroyed many systems, including a hydraulic system, the anti-lock braking system, flaps and electronic controls.
After emergency landing, the pilots were unable to stop engine number 1, because the controls had been destroyed by shrapnel. Emergency services had to douse the engine until flameout was achieved.

Source