Now you can assess the true condition of the finish. Gelcoat shines because it's a smooth surface that reflects light. Even microscopic irregularities can diminish that shine, but those same irregularities may be restored with just a sealing compound, or a very mild polish such as Star Brite's Premium Marine Polish with PTEF. Pick an area to test. If two or three passes with the polish don't yield the desired results, move to a mild abrasive polish like Meguiar's Premium Cleaner/ Wax or Color Restorer. If oxidation is heavier, and cleaner doesn't do the trick, only then should you consider a cutting compound. Again, start with a less aggressive formula like 3M's Marine Rubbing Compound, and move to a more aggressive compound such as 3M's Marine Super Duty Rubbing Compound only as a last resort.