If the device is showing no signs of life (no lights and no internal sounds), try option 1. However, if there are any signs of life (lights on, internal fan or drive sounds, etc.) then try option 2.
Option 1...
NOTE: Yes, I know some batteries are not so easy to get to, on some devices. However, it should be removable/replaceable. Unless it is under warranty, then you should contact the manufacturer first.
Try the following and see if it will turn on...
1. Unplug your charger cord.
2. Remove the battery.
3. Press and hold the "Power" button for 30 seconds.
4. Now plug back in the power/charger cord.
5. 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...