What is true of the ages of normal stars, compared to those which do not produce energy by this process?

Proton fusion is the main energy source for stars with less than about twice the Sun's mass.  Such stars have longer life spans than more massive stars and cannot nova.

If I understand well, you mean the difference between Main Sequence stars and massive stars. The first are the more numerous in the universe and the sun is one of them. Also Red Dwarfs are main sequence stars, but are very small compared to our sun and last, therefore, up to a trillion and more years while stars like our sun last only billions of years. These stars obtain fusion reactions through the proton-proton chain to yield helium.

Massive stars, instead, go through the C-N-O cycle (Carbon-Nitrogen-Oxygen) to produce helium. These stars have short life periods. Very massive stars last only a few million years! 

I don't always try to answer unusual questions on Yahoo! Answers, but when I do, I drink Dos Equis. 

If you mean white dwarf stars, billions to trillions of YEARS. All stars get energy from nuclear fusion at some point, including white dwarf stars before they became white dwarf stars.