Yes the keyboard and mouse etc could light up and work due to low power draw, when the GPU and CPU being to take in more power it could cause the PSU to act up, I've had a faulty PSU that I could get into windows with, browse YouTube bit as soon as I played a game or did anything like that the PC would crash, the PSU did this on different machines as well but after a new PSU was in place everything was normal.
Have you got a warranty on your PSU or CPU? Could you easily sent it to the supplier for them to check?