I have this problem before when playing my 360 with my almost 4 years old CRT monitor. The monitor's VGA cable has spoiled, causing the color displayed to be distorted. Since the cable on my CRT monitor can't be replaced, I switched to widescreen LCD and no longer face the problem.

My advice:

1) Try your 360 on other monitor, if it works fine, then something is wrong with your monitor.
2) If the problem still exist when tested on other monitor, try borrowing and change the 360's VGA / Component cable you're using. If the problem still exist, then the problem probably come from your console.