I can't say what has failed with 100% accuracy, but since it gradually got worse (I'm assuming), I'd suspect a failed/failing coupling capacitor in the video output section/s of the XBOX. Find someone with electronic knowledge if you don't feel 100% around PC boards and soldering. You could try a little freeze spray on each cap in the area while watching the video, look for one that's swelled or leaking, or temporarily jumper the suspect cap and see if you have improvement. I doubt that any IC or semiconductor has failed.
Hope this helps.