Have you tried the following....
1. Remove the power/charger cord.
2. Take the battery out.
3. Hold down the power button for about 30 seconds.
4. Now it should turn on.
5. Once it has, plug in the charger cord first... then if all goes well, put the battery back in.
If this doesn't help, you might want to try starting the computer in "Safe Mode". To do so, shut it off, and then when you turn it back on, continually hit the F8 key until you get the menu where you can choose to load in "Safe Mode". If the computer loads, then you know you have something on it that is messing with it (virus, etc.,).
If it isn't that, then you may need the display replaced, should it turn on but not show you anything.