When the laptop screen goes black, can you see the power/drive light blinking or just everything remains calm and nothing can be heard from the fan or the hard drive? If you can't and the warranty of your laptop has already expired I suggest you to take out the hard drive and try to connect it to another computer through SATA-USB cable. If the HDD doesn't spin at all, anywhere, then it has failed mechanically and needs replacement.
If your hard drive spins up on a different computer and it is recognized there, but cannot power up on your laptop, then the problem is hiding probably in the power supply unit on your motherboard. You could bring your laptop to a technician to make a test of the power connector and/or the power jack center because they might have got damaged.
If only the display shuts off but the laptop is still running then the problem that you have might be due to the failure of the video chip. Sometimes, after much of a use and less cooling the graphics processor which is responsible for video signal transmission get unsolders, the thermic paste goes away and it gets unsoldered, therefore the screen doesn't show anything. If you possess knowledge of notebooks' hardware you can change the paste yourself by opening the laptop and check if the chipset that is next to the processor has got unsoldered or you can bring your laptop to a technician to get it soldered again.