Sounds like a bad battery but sometimes if the battery is too flat it will cause this.
So what I do is hold power + volume down + home until you get the text prompting you to go into download mode warning.
Leave it on that screen while plugged into charger for about 30 minutes and that will charge the battery enough to get it on if it is not turning on because it was flat.
Once it's been charged for 30 minutes press the corresponding button to reboot tablet when prompted.
If this is still no good I recommend reflashing the firmware which I will write instructions on how to later when I have time.
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