In most cases, the battery is just drained. Charge it for a little while, maybe a minute. Then, turn it on. If that doesn't work, the cause could be coming from the power button itself or the battery. This link provides a more detailed approach to troubleshooting the problem you're having: Nobis NB07 Troubleshooting.
The outlet that you're using could be bad. Try plugging the charger into another outlet. As for the charger itself, check to see if there's any damage like frayed wiring or loose parts. You might also want to check the battery to see if it is positioned incorrectly. It could be a bad battery as well. This link will give you a little more info on troubleshooting the problem: Nobis NB07 Troubleshooting.
Sounds like it may be a software glitch. There are many things that could cause a software glitch including the maximum amount of memory being used. The simplest step would be to hold the power button to reboot the tablet. If this doesn't work, try connecting the tablet to the charger or a computer and rebooting it again. If the tablet is still unresponsive, push and hold the small reset button on the backside of the tablet until the screen changes. Otherwise, open the tablet and remove and reinsert the battery. There are troubleshooting steps regarding the issue you're describing that can be accessed with this link: Nobis NB07 Troubleshooting.