Why is my screen still off when I press power button?

I have issue with my ASUS N56VZ, when I press the power button the screen doesn't seem to turn on while the fan and the indicator lamp is on, changing the RAM still not fixed it. I have tried to connect to external monitor but didn't work either. This issue happens gradually, at first couple of days the laptop works when I hard restart couple of times, but eventually it's completely off. Does anybody have any idea for this issue ?appreciate for any comments, thanks a lot.