Many years ago I scavenged some old Corian counter tops a neighbor was throwing out. They were in fairly rough shape with lots of cuts and scratches. I treated it just like it was a piece of wood and started sanding with progressively smaller grit sand paper going up to 1200 grit wet/dry paper. As a final step, I used some rubbing compound with a heavy duty Dewalt polisher. The Corian looked like brand new when I was done.