Is it actually staying on (lights on, internal sounds, etc.) but just the display is black? If that is the case, try the following...
Turn the laptop off (not sleep or hibernate but off).
Connect an external monitor to the laptop.
Turn on the external monitor.
Turn on the laptop.
NOTE: You may have to press an "external monitor" button. Could be the f4 button or a button with two monitors on it, for the external monitor to work.
If you can see fine on the external monitor, then your attached display, or the ribbon cable that connects it, are your problem.
If you can't see on the external monitor at all, or the problem occurs on the external monitor as well, then it is probably the graphics card/GPU that is the problem, which may require the motherboard be replaced.
You may also want to try hitting CTRL + SHIFT + WIN + B to try and reset your graphics driver as another possible fix.
This can be caused by (depending on the laptop model, you didn't say what model you have) a faulty backlight power inverter, faulty backlight power cable, faulty lid switch, faulty video cable or faulty screen.