Word or phrase that means to ascertain whether someone is alive or dead

Solution 1:

Not sure there is a single word for this- 'triage' is possibly more apt than diagnose as it has more of a sense of life and death. However, it also does not result in a binary classification.

Solution 2:

Triage ("the process of determining the priority of patients' treatments based on the severity of their condition ... from the French verb trier, meaning to separate, sift or select") has been mentioned, but I'll write a bit more about it anyway. The wikipedia article on triage says

At its most primitive, those responsible for the removal of the wounded from a battlefield ... have divided victims into three categories:
• Those who are likely to live, regardless of what care they receive;
• Those who are likely to die, regardless of what care they receive;
• Those for whom immediate care might make a positive difference in outcome.

Techniques of triage are taught in medical school (during emergency-room or critical-care rotations) to allow coping with catastrophes.

Solution 3:

For devices in computer networks, ping is the common word.

Ping the server to find if it's busy.

For human beings, check or check up stands for this meaning and is also easily understandable.

The doctor checked his pulse to ascertain his death.

Solution 4:

It's not one word, but viability check may fit your bill