I removed scratches from my corian counter top with very fine sand paper. How do I replace the counter top sheen in these areas?

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You need to call the corian people and ask for sure. Most likely they will tell you to call a professional so you don't caus further damage. It will take a buffing wheel and compound to get it out and back to luster.

There are a lot of unknowns here.

What grit did you use. Very fine does not define it.

Another unknown is what your luster was. This is tough to tell verbally.

Typically a satin finish is achieved by sanding with 400 grit sand paper followed by a grey Scotchbrite.

A higher luster would be achieved by following that with 800 or 1000 grit sand paper and a white Scotchbrite.

Hand sanding and power buffing with the scotchbrite.

Here are some things to read: Caring for DuPont? Corian® (http://www2.dupont.com/Surfaces/en_US/products/corian/corian_care.html)
How to Polish Corian | eHow.com (http://www.ehow.com/how_4896153_polish-corian.html)

Pattyg2,

The duPont piece seems a little confusing though accurate. It has a lot of options.

The eHow piece is badly written. The author never completes a thought. It is also quite wrong.

I have always used scotchbrite pads and done it by hand, it takes elbow grease but the smaller scratches will come out,, the finest sandpaper 1000-1200 or something would be best of you haven't already tried that.