Cactus is turning yellow at tips?

I have a very large cactus I have had for many years....its had a hard life....moving from place to place, very little sunlight at times, sometimes in a very dark basement for the winter due to lack of windows and sunlight....I am in a new residence and I am worried about it because when I moved in I put it outside in direct sunlight, I covered it up for fear it would burn or die...it was pretty warm out then , then the temps dropped to the high 3os at night..>I covered it up moreso....I worried it will die faster now.....it has started to turn yellow at one tip of the cactus, shriveled up too....I dont know what to do , do I cut this off? I dont know what the cause is...from low temps, from direct sunlight or it being root bound which it may be....any suggestions to help my poor KILLER cactus will make me very happy.