Why is my iPad unresponsive to the power button?

I suggest that you put it on charge for at least half an hour, then, keeping it plugged in, try a "forced" restart of your iPad, using these gestures:

• On an iPad with a Home button: Press and hold the power button and the Home button at the same time. When the Apple logo appears, release both buttons.
• On other iPad models: In rapid sequence, press and quickly release the volume up button, press and quickly release the volume down button, then press and hold the power button. Only when the Apple logo appears (it might take 10-20 seconds), release that button (ignore all other screens that might appear, the one with the "slider" to turn the device off included).

If the issue persists, contact Apple Support, using this link:--> Contact - Official Apple Support

Regards

Giulio

Then it seems like that your iPad is in need of service I am afraid. Please Contact - Official Apple Support to set up service for your iPad