Is there any reason you cannot make a warranty claim?
Keep it plugged in for a W H I L E (like, 24 hours), then unplug it, and experiment with attempting to power on the switch while plugging/unplugging the system. To me, this sounds outright defective.
EDIT; I made the same comprehension error as the user above me, however, my advice is unchanged. If that doesn't work I'd ask questions like, have you dropped it recently? Or, better yet, did it drink Kool-Aid?