First thing to do is to reboot into Safe Mode and see if the problem still occurs. If it doesn't then some 3rd party application that you've installed is keeping the device awake (and presumably the screen on, if that's what you're describing).
To reboot into Safe Mode, long-press the Power button until you get the 'Power off' prompt. Then long-press the prompt until you see the 'Reboot to safe mode' prompt. Select 'OK' and your device will reboot in Safe Mode; once you're done checking for the desired behavior you can power off and power on and the device will boot normally.