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, 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.
From there, if it is still not working, then you may need to open it up and find out the problem. Or take it to a local tech/repair shop.