Are you sure it isn't actually on, and just the screen isn't on? Are there any sounds coming from inside it. Hard drive, fan, etc.? If there are, then it may be the display and not the power.
Try this...
1. Turn the laptop off (not sleep or hibernate but off).
2. Connect an external monitor to the laptop.
3. Turn on the external monitor.
4. 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.