my iPhone screen is black (no light),

Then either turn up the brightness or make an appointment at the genius bar and take it in for service.

Out of batterie power?

Hey, this just happened to me also. I tried to restore the phone with ITUNES but it wouldn't let me because it was asking me to accept the ITUNES request on my phone, which was black. The next thing I tried worked. Use the Apple Find my phone application and use the erase feature. It seems drastic but better than going to Apple and fighting the lines. Now after you have done this you can restore you phone to its newest state either with the ICloud backup or ITUNES.