rayray: It should be noted that this is one of the earlier elites, possibly from their first production run. I would hope that the box you bought was manufactured using some of the newer processes. Anyway, if there is a problem the warranty covers it. Just make sure your xbox has the appropriate amount of ventilation.
Paulius: It's a good suggestion, but yea, I tried that. The cable is HDMI, which is a digital signal, so usually if the cable is bad you get no signal at all (unlike say VGA, Composite, or Component video which is all analog). The Xbox 360 also has an error code (all four lights blink red) if it is having problems with the video cable, although whether or not this would detect a faulty cable I don't know.