BTW cleaning the dvd drive rarely helps for the problem you're describing. Buy a new xbox, and swap the dvd drive if you don't want to lose all your downloads/saves. That's what I did. I then used the old xbox with the failing dvd drive as a dvd player for the bedroom. It worked fine with movies, despite screwing up on games.
Another option is to buy another drive to replace yours. There are 3 different drives available for the X Box, you can get one ranging from $50 to about $100 or so. Go <a href="http://www.llamma.com/xbox/">here</a> for tutorials on how to remove the drive and to see what parts you can order.