Most people usually think that there's a problem with their CD Drive but follow the steps to make sure:
Put a movie in your Xbox 360 console. If it works, then your drive is working properly! If not, then you may have to change your drive, but whatever happens, try the following. If the problem is not solved then change your CD Drive.
Go to Settings -> System Settings -> Storage (and select your hard drive WITHOUT clicking on it!)
Type as fast as possible LB, RB, X, LB, RB, X
A message saying about deleting the last update should appear. Make sure your console is connected to the internet! After the console restarts (it will take about 5-10 minutes), a message would show up saying update required. Press yes and wait.
This may fix your problem. It's just a solution that worked on my occasion.
