SP315-51 : Screen won't turn on

I had left my laptop open last night when I went to sleep. I wake up and close it and head to school. I open it and it seemed like it never turned off while it was closed, the computer was warm and the screen was still the same screen I woke up to, not the start up screen.
It wasn't responsive, not to touch, keyboard, or trackpad, so I turned it off thinking it'll just reboot.
When I turn it on, the keyboard lights up, like normal, but there's no welcoming screen, or any screen at all. Just a unlit black screen. The fans start a little bit later, say 30 seconds or so, and soon after turn on, it turns off for a second, and if the power supply is in, it turns back on without any touch, if the supply is not plugged in, it won't turn back on.
I've tried restarting it by just holding the power button until it turns off, then turning it back on, and I've tried the little battery hole in the back, holding it down with a paper clip for 5 seconds, and I've tried holding down the power button for 30 seconds.
Right now, it's plugged in to the power supply, the fan is running, and the keyboard is lit up. But still no screen.

Any ideas on how to fix this? I still have a year warranty on it, I had just got it this summer, but to whom do I send it to be fixed?