2005 Chevy Cavalier Check Engine Light Will Not Shut Off

I just purchased a used 2005 Chevy Cavalier with 52,000 miles on it from a major and reputable car dealership. I had the car for only 2 weeks and I noticed that the "check engine light" stays on while the engine running. I have only driven the car a few times since purchasing it. The car's owner manual said to check and make sure the gas cap wasn't loose. I have removed and reinstalled the gas cap on numerous occasions -- the "check engine light" will not go off. The car apparently passed a "dealer's" (I'm assuming) vehicle inspection 3 days prior to me buying it. The car was equipped with a new vehicle safety inspection sticker. I have read a lit "check engine light would be grounds for an overall "FAILED" vehicle safety inspection. If the problem isn't with the gas cap, it has to be something else. I really don't know if the "check engine light" was on the very first time I drove the car home. The light is amber in color and I probably just overlooked it while focusing on driving. All of the many other dashboard lights go off after the engine is started. The car has spent more time in my garage than out on the road. The car appears to be running great, other than the problem with the lit "check engine light."