I have been working with Corian and other solid surfaces for almost 18 years. THe sheet is finished using a random orbital sander with combinations of scotch-brite, sandpaper, and Trizak papers.
The beauty of solid surface is the repairability.
It also depends on the actual brand of solid surface you have and the ratio of acrylic to polyester resin in the material.
I would recommend contacting a solid surface shop and scheduling a re-buff. I have clients that schedule the shop to come out to their homes once a year and re-buff the top back to factory shine.
Here is some information if you want to attempt it yourself.
Sanding and Buffing Solid Surface Countertops
Pay close attention to the discussion of direction and movement of the sander. You can create pigtails or even divots if done improperly.