Does the clock make any noise at all? That is, does it beep when you do the countdown?
If yes, then we know the buzzer works.
Are you sure you have the clock and alarm set to the correct AM or PM? That is, if you have the alarm set for 2:00PM, are you sure the clock time is set to PM? Remember that when the clock time is set to PM, the PM indicator light is not on. The PM indicator light is only on when you are setting the time using the hour button.