It’s got to be turning on if it is recognized and seen by your computer. Your computer won’t ‘see’ it if it’s not powered on.
So, it sounds like JaZZ’s suggestion is valid. Make sure you have peeled off the screen protector film. It has an screen-shot image on it making it ‘appear’ to be on when it isn’t. But it covers up the real screen, so you can press buttons till you’re blue In the face and that image won’t change and you can’t see under it.