The red light is a battery indicator. If it is lit, the batteries are good. Try changing lenses. If the shutter on the different lens works correctly then the lens is the problem. If there is no change, the problem will be in the camera body. Most likely with the electrical contacts on the shutter speed selector.

Best of luck.

P.S. Definately download the manual, if you haven't already, as Jon suggested. There are a lot of buttons and switches on these cameras that don't have much for labels describing their function.