Yes this error can be fixed .. depending on what it is , Ok we know its a dvd drive error , could be a few reasons though, has the console ever had hacked firmware flashed to the drive ? If so it could be a problem with that, or the dvd drive is actually Kaput. You can change the DVD drives in Xbox's for different versions, it all depends on your skill level, for me it's easy because i have done a few and repair/modify xbox's all the time. If you have never even opened a 360 then it will be a bit tricky, google replacing xbox DVD drives and get a bit more info.
Slim