There are two likely faults with three possible fixes.
The most likely fault is a crash, which could be resolved by holding down the power button until the screen turns back on.
If that does not work you may need to restart the device by pulling the battery. Which can be done by following the first two steps of this guide.
Kindle Fire HD 2013 Battery Replacement
The last option is a screen replacement, which can be completed by following this guide.
Kindle Fire HD 2013 Screen Replacement
I hope this helps,
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