How to tell if a tooth is not dead?

See your dentist. Temperature sensitivity (cold) is often the easiest test to determine the vitality of a tooth. But for a person to do on there own may be difficult and lead to false interpretation as the cold may overlap onto adjacent teeth thereby making your own diagnosis difficult. Let your dentist evaluate your teeth, or go to university of iowa dental school.
Sensitivity. If the tooth in question is sensitive to cold and possibly sweets, then it is definitely vital.