The screen randomly went black

I know this kinda sounds strange because of it being a random thing that happened but the small cable that runs up the side and connects to the camera/2D-3D buttons comes unplugged from the main board quite easily. I say this from experience had the same phone was working fine then it started to heat up insanely fast and had a bunch of software errors that were happening all the time basically rendered the phone useless. Upon taking it apart the first thing I noticed was that the button cable had come detached from the main board. Plugged it back in, reassembled phone and worked just like new again. Just something I would check for since you said it was getting hot.