I am in the kitchen business and know Corian very well. It is a wear surface and polishing it will only make the inevitable surface scratches more noticeable. Until people over did it, corian used to include a package of Comet in their owner's package and tell you to wash the top down with an abrasive cleanser like that all the time which gives you a fine matte finish which makes it look good and not scratch prone. When a top is scratched up and in need of a fresh start, the service guys will sand as noted by another poster and then finish off by putting some comet under a scotchbrite pad and using a vibrating sander to give it a nice consistent finish. Unless you have a mess, just start washing with an abrasive cleanser and in no time it will all have a nice patina that is easy to care for.
If you decide to sand, be very careful not to stay in one spot and create hollows which are very hard to get rid of.