If you don't like paying $9 for Bondo, you probably won't like the way I'd do it: cut off the broken corners, then make a new piece of wood that's an exact match. I'd route groves in the cabinet and the replacement piece. I'd insert splines in the grooves, glue and clamp the whole thing to the cabinet, as well as screwing through the replacement piece into the sides of the cabinet. Chances are you won't get everything perfectly aligned, so I'd then cover the joints with Bondo and sand the whole area smooth. Finally, I'd buy custom-matched paint and repaint the affected area.