1999 GMC Sierra Truck won't crank or start

When I turn the key, the engine won't crank or even try to turn over. I've tried putting the transmission in each gear and it's the same for all. My battery is new and has plenty of juice. I do hear a 'click' in the fuse panel when I turn the key and I also get a 'click' when I depress the brake pedal. It seems that the electrical connections are fine. Would this be the neutral safety switch? And if so, is it easy to locate and replace? Any help would be greatly appreciated. Thanks!