If the phone won't power on, make sure the battery isn't completely drained.
After you have confirmed the phone is charged, try to power it on by pressing and holding the
button for 10-15 seconds.
If the phone still doesn't power on, holding down certain hardware buttons can force the phone to reboot. See
How do I reboot the phone using hardware buttons? for details.
Note: Some phone models may not have a notification LED.