We've seen this happen on rare occasions. You can try one of the following two methods to recover:

1. Hold down the power button for at least 10 seconds. The screen will stay black.

After releasing the power button, wait 3 seconds, then press the power button again for 3 seconds. 

The tablet should power up now.

2. If the first method doesn't work, there is another possible button sequence you can do to revive your device...

For the nVidia Shield -

  1. Press and hold the Volume Down (-) button

  2. Press the Power button while continuing to hold down the Volume Down (-)
  3. Release the Volume Down (-) after 5 seconds or when you see a small menu appear on the screen

  4. Highlight the Continue option using the Volume (+/-) buttons
    - unfortunately, the menu text is very small...
  5. Press the Power button once to select - your device will then reboot as normal!
** if you are still unable to power up your device, please contact support.