I've read numerous forum posts and mini-articles about substituting applesauce for oil in brownie mix, but for some reason it went horribly wrong:    (Okay, that's actually after trying to salvage it by putting it back in the oven after grabbing some good slivers off the edge) 
Yeah, something just looks wrong there!  Why are the edges so cooked and yet even an inch from the edge it's still completely wet? I have to imagine it's under-cooked like rfusca.  However, from the looks of it, cooking it til the center is done would burn the edges.  My advice: try it again, but make one batch with oil (per the box) and make one batch with your 100% applesauce substitution.  Bake them the same amount of time, in the same oven, on the same rack, in similar pans (if possible), and at the same temperature.  When you test for doneness, check about 3-4 inches diagonally in from a corner.  A toothpick should come out dry.  Don't check directly in the middle... by time that's dry, the rest of the brownies will be overcooked.  By that point, you should have a good understanding of the problem source. 