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See this, If your iPhone, iPad, or iPod touch won't turn on or is frozen - Apple Support

And this is the last steps in the support document that I provided you.

If you need more help

Contact Apple Support to set up service if you have any of these issues:

• You still see a black screen after charging, force restarting, or following the steps in this article.
• You see a black screen, but you can hear alerts, sounds, and vibrations.
• The screen remains black, but the device chirps when you unmute it and connect it to power.
• Your screen is on, but it doesn't respond when you tap, slide, or try other gestures. 
• You can't force your device to restart because a button is broken or stuck.
• Your device is stuck on the Apple logo, displays a solid color, or isn't recognized in iTunes.

So, you need to contact Apple Support. Use the link you were provided.