In most cases death is diagnosed when there is no pulse, heart sounds or breath sounds over 1 minute. Tjhe case of a coma is different, when two experienced doctors agree that all brainstem function has ceased even if the heart is still beating. You have to be ventilated for this to be the case.
Officially when the brain stem dies. However The brain dies four minutes after the heart stops due to lack of blood thus lack of oxygen. So unless there has been CPR performed, four minutes after the Carotid pulses stop, the brain dies.