If the damage was a scratch, the sanding and polishing should have solved your problem. If the damage is a crack you have a much bigger problem. Corian is an acrylic product and, as I understand it, is repairable using catalyzed acrylic glues. Some repairs are done by routing out the crack and sealing with new material. It is not likely a DIY repair.
There may be a reason the contractor never used the Corian, it was severely damaged and may have been replaced under a warranty. You got the salvage or scrap. I believe the cracks can be sealed, but it is going to be very difficult to make a permanent repair that won't show discoloration over time. You might check whether a warranty can be applied at www.corian.com.