Have you tried plugging it in to charge and leaving it on the charger for a few hours? If it doesn't charge, then I would check to make sure the charger cord isn't the problem.
If it charges but still won't turn on, try pressing the power button for about 30 seconds or so, then let it go and then press power again.
Before doing anything other than those mentioned above (should they not fix the problem), if the device is still under warranty, I would contact the manufacturer or the place where it was purchased.