Sometimes folks have found an offending app like netflix can lock up the CPU so it is no longer responsive to the power button. For this situations press and hold the power button for 30 seconds an the unit should reboot.
There is a separate problem where if the tablet is drained of battery completely, sometimes it will not turn on until it gets some trickle charge. Leaving it attached to the power adapter a couple of hours usually resolves it, but sometimes it will only accept lower amp charge so try the USB port on a computer too.
Disclaimer: No touchscreens
were harmed nor injured during the creation of this post. GPS
units were all treated ethically and humanely.
Signed: People against misbehaving Nexus 7 2013s