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.
5. Now plug back in the power/charger cord.
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.