Leave the phone on the wall charger (not USB) for several hours (overnight) and try to power on again.
Also, try to boot into bootloader: Hold power and the volume down rocker for a few seconds. Let go of power but DO NOT let go of the volume down rocker until the white bootloader screen comes up, or until you are convinced the phone is still unresponsive (a minute or so).
Is the phone stock or modded?
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Phone: HTC One X (AT&T version) Rooted, Bootloader Unlocked, S-Off
Tablet: Samsung Galaxy Note 8 (WiFi only) Rooted