Motorolas Moto E, Moto G and Moto X have non removable batteries. So if the phone is stuck and not responding to touch as well as buttons, do the following to force it to restart.
Press "Power Key" and "Volume Down Key" simultaneously and hold them pressed for 10 seconds, the phone will be forced to reboot.
Note that this combination of buttons takes a screen shot of what is displayed on the screen. Do not get confused, even if it takes a screenshot(or you have heard screenshot capture sound), continue to hold the buttons for more than 10 seconds and the phone will be restarted. In case the phone fails to restart after 10 seconds, make a second attempt of 20 seconds.
In case you see "AP Fastboot Flash Mode" while restarting, press the "Power Key" once and the phone will boot up normally.