Can helicopters have engines running while rotor blade stays stationary? So, I was skiing sometime ago, and unfortunately, another skier got injured. So, a heli was flown up to get the injured skier. The rotor blades were stationary, but I still heard some sort of engine like sound. Does anyone know any helicopters capable of doing this sort of thing?
Yes, many helicopters (but not all) can do this. There are 2 main methods: 


a clutch between engine and rotor system
for turbines only: a rotor brake on the engine output shaft. The engine contains a free turbine (i.e. a turbine stage that isn't attached to the compressor) that drives the rotor system. If you brake this shaft, the engine can run without spinning the rotors.