Before you post here about problems with your console's AV outputs here is a brief trouble shooting guide
1. Test the console on the same TV at the same resolution using different AV cables (borrow from a friend or something)
^this will determine if the av cables are the problem
2. Test the console on a different TV with the Same cables running at the same resolution (take it to a friends house or something)
^this will determine if the TV is the problem
3. Test a different Xbox 360 on the same TV with the Same cables (borrow from a friend or rent one)
^this will determine if the Xbox 360 is the problem
4. If the problem only occurs in one or two games then try getting another copy of the game (borrow from a friend or rent them) and see if the problem still exists using a different copy of the same game.
^this will determine if the disc is the problem
If the problem still persists in all of the steps above be sure to include the results of each test in your post, if anything changed from one test or another, even if you don't have the resources to perform all of the tests post the ones you were able to try and what changed, if anything. Don't bother lying either because you'll only make it harder to find a solution to your problem.
If you're having trouble deciding the best resolution to use or the best type of cable to use be sure to include the MAKE and MODEL of your TV or Monitor, preferably with a link to the manufacturers page and or a spec sheet. No one will be able to help you if you don't do this. BTW: no one cares how big your screen is, or how much you paid... that information is completely irrelevant to solving your problem.