Is the laptop actually on (you can hear fan, hard drive sounds etc.,) but just the screen is dark? Or is it not turning on at all?
If it is just the display, then there are a few things to try. First, turn off the laptop, connect an external monitor to the laptop, turn the external monitor on, and then turn on the laptop. Can you see your desktop on the external monitor?
If yes, then the connected display is the issue. You should then look inside to make sure that the ribbon cable that connects it isn't loose, dislodged, damaged, bent, pinched, etc.
If no, then it may be your graphics card/GPU, and possibly the motherboard needing replacement.
NOTE: If this laptop is still under warranty, do not do any work on it inside, don't open it up, and contact the manufacturer about a repair or replacement.