If your TV makes picture from a different console or for your cable itself then it is your xbox. If not, your tv. Simple as that. Do a quick test, put something else on the tv or the xbox on a different tv.
Neither...Go to best buy, you will have better luck there if you are looking to just buy. I think you could go wiht just an HP or ASUS desktop. Make sure it has at least an 8000 series Graphics card (Nvidia) Or An HD 4000 series for ATI good luck. You also want at least an intel core 2 duo...