How long would it take to die breathing pure nitrogen?

Depends entirely on blood O2 saturation prior to exposure to the Nitrogen. Given a 100% Nitrogen atmosphere, the expected time with zero oxygen, starting with a normally O2 saturated victim is about 9 minutes before mortality. However, severe and permanent injury can occur in a shorter timeframe -- as little as 4-5 minutes. Note that extreme hypthermia may cause a significant increase in these times.