I am sorry to hear you are having this problem. When these sort of errors occur, it can be a result of one of three things;
1. Data on the console
2. The disc
3. The console itself
As you have already cleared the cache and it's still skipping, this removes the possibility of data on the console causing this error.
I recommend that you try your game disc on a different console (friend, family, retailer). If the same thing happens on a different XBox, then the issue will be damage to that disc. However if the game plays perfectly fine on a different console, then you may want to contact Microsoft to assist you with your console.
If the disc is damaged, you can file a warranty replacement for the game at http://warranty.activision.com.
Try going here and trying this http://community.callofduty.com/message/205575481#205575481. I know some systems that if the games RPMs are below a certain point or something minute such as that can cause this