I know this is probably too late for you, but I have seen an issue with this tablet where it is actually turned on but the screen doesn't light up. You can tell this is happening because if you keep pressing the power button (holding it to initiate a shutdown) you here the beeps from the pop-up window confirming if you really want to turn it off.
If you press on the edges/slightly twist the tablet you can get the screen to turn on again and it will work fine for a period of time.