Replacing a garbage disposal is fairly easy. I've done it twice.
But before you consider replacing it, it is possible that the fuse (or whatever) on it has trigger. The GD's I've seen have a little switch on the bottom to reset the fuse, much like a GFI outlet.
But first make sure there is nothing clogging the disposal. I once found a screw that had fallen into the disposal. It got trapped in one of the little holes and was blocking the blades. So unplug the disposal first and then see if you can dig out whatever is inside the thing that is causing the blockage.