See if it will start up in "Safe Mode". If it does, then you need to check the tablet for viruses, malware, bad apps, etc. If it still won't start even in "Safe Mode", then I would have a tech look at it (or contact the manufacturer if under warranty.
To get into "Safe Mode" please do the following.
1. First turn off the tablet.
2. Next press and hold "Power" until you see the manufacturers logo on the screen, then release the power button.
3. "Quickly" press "Volume Down" and hold it for few seconds until you see the message "Safe mode: ON" or something similar.
4. If you wanted disable it, simply repeat the steps above, and you should see "Safe Mode: OFF" rather than on.
I am confused here. If it is completely drained of power, it should turn totally off. No signs of life. Are you then plugging it in to charge and it comes on automatically? Or are you letting it charge and then when you try to start it it keeps restarting itself?