|MadSci Network: Astronomy|
You are right that the light from the sun is not red-shifted, at least not from our point of view. It is the movement of the source of the light, depending on your frame of reference, that gives light a red or blue shift. The night sky is black because there is no light. It would seem that the sky should be bright white because of the billions of stars and galaxies in the universe. The problem is that all the billions of stars are billions of miles apart; space is mostly that, empty space, which does not produce light. Plus, the intensity of light, that is the energy which is responsible for light, decreases inversely with the distance squared. This means that the brightness of light from any source drops off quickly over distance.
Try the links in the MadSci Library for more information on Astronomy.