Apple devices such as iPods and iPads have a deep sleep mode that they go into when the battery gets very low. When they are in this deep sleep mode, it appears that they can't turn on.
To bring an iPad or iPhone out of deep sleep:
- Hold home button (lower middle) and sleep button (upper right edge) for 10 seconds
- Hold the sleep button (upper right edge) for about 10 seconds
It may also help if the device is plugged into power when this is performed.
We've also seen some of these devices go into this deep sleep mode for no apparent reason. I suspect an odd user button combination, but can't tell for sure. So, even if the batter charge is OK, this may be your issue.