Are you sure it is actually not on?
Are there any sounds at all coming from it. Fan? Hard drive? etc? If there are, but the screen is blank, it may be a display issue and not the whole laptop. If that is the case try the following..
1. Turn the laptop completely off.
2. Connect an external monitor to the laptop.
3. Turn on the external monitor.
4. Turn on the laptop.
If you can see anything on the external monitor, then the attached display is the issue.
If you can't see anything on the external monitor either (and the computer as I said above is actually on per sounds) then the graphics card/GPU is the issue.
Now if there are no sounds at all, try the following and see if it will turn on.
1. First make sure the device has been charged.
2. Unplug your charger cord.
3. Remove the battery.
4. Press and hold the "Power" button for 30 seconds and see if the device will turn on.
5. If it does, great, if not yet, no big deal. Now plug back in the power/charger cord. (If it didn't turn on without the cord in, it should turn on once you it is in. Yes sometimes they will turn on, or try to turn on, even with nothing attached/plugged in.)
6. Now put the battery back in.
If this doesn't help, then test the power cord to see if it is good. Either try your cord in another device, or try another devices cord in your laptop.
Should that not be the problem, then check the battery to see if it needs replacing.