To dream of an alarm clock is your unconscious letting you know that an important time is drawing near.
To dream of the clock going off but you are not responding is a reminder to keep to your appointments in the near future so as not to miss a vital piece of information.
Dreaming of an alarm clock that doesn't work shows that you may not be valuing another's time and effort could be made to show that you are in fact grateful for all that they do for you.