Frozen? it won't do anything after I turn it on - it's frozen

Hello

"Performing a hard reset on your Kindle Fire may resolve intermittent issues like a frozen screen, battery issues or trouble downloading content to your Kindle Fire. Allow your Kindle Fire to charge for approximately 30 minutes, then try the following steps.
To perform a hard reset on your Kindle Fire, press and hold the power button for 20 seconds and then release. After the device has completely turned off, press the power button to restart your Kindle Fire.
If your Kindle Fire is still unresponsive, try charging your Kindle Fire before trying to reset the device again. Hope this helps, good luck.

For more query visit us: Kindle Fire Support

Click on the link to get the solution for your frozen screen............
What You Can Do To Resolve Frozen Screen Issue On Kindle Fire HD Device

Maybe the Kindle is frozen on that screen. The Kindle HDX User Guide suggests a hard reset by holding down the power button for 20 seconds before releasing it. That should shut the Kindle down. Be sure to not have the Kindle on a charger or hooked up to a USB cable during the hard reset. Next restart the Kindle. If that fails then charge the Kindle as you would normally do and when done detach the charger and USB cable and try another hard reset. If all fails go to www.amazon.com/kindlesupport.

Patricia, Using the power switch, you can forcibly reset your Kindle device. This reset will shut down the Kindle without accessing the shutdown command from within the Kindle's operating system, a particularly useful tool when dealing with a frozen Kindle. To initiate a hard shutdown, Kindle disconnect from its charger, slide and hold the power switch for about 20 seconds. This will force the Kindle to shut down, now it can be restarted normally.
Check links below for charging problems.
"I hope this helped you out, if so let me know by pressing the helpful button. Check out some of my other posts if you need more tips and info."
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Try again. Make sure Kindle is charged. Hold down the on button until you see the fire logo. This usually works.

Restarting Kindle Fire may resolve intermittent issues like a frozen screen, battery issues or trouble downloading content to your Kindle Fire.
To restart your Kindle Fire, press and hold the power button for 40 seconds and then release. After the device has completely turned off, press the power button to restart your Kindle Fire.
If your Kindle Fire is still unresponsive, try charging your Kindle Fire before trying to restart the device again.
Make sure you have the latest software version available installed on your Kindle Fire. The latest version is available at www.amazon.com/kindlesoftwareupdates

"Performing a hard reset on your Kindle Fire may resolve intermittent issues like a frozen screen, battery issues or trouble downloading content to your Kindle Fire. Allow your Kindle Fire to charge for approximately 30 minutes, then try the following steps.
To perform a hard reset on your Kindle Fire, press and hold the power button for 20 seconds and then release. After the device has completely turned off, press the power button to restart your Kindle Fire.
If your Kindle Fire is still unresponsive, try charging your Kindle Fire before trying to reset the device again." from here. Hope this helps, good luck.

I assume you've tried holding in the power button for 30 seconds?
Leave your Kindle on until the battery dies and then recharge it.
Failing that, contact Amazon - they replaced mine immediately and without quibble.