Sorry just wanted to discount the easiest possibilities first.
1. Have you ever got the Xbox working with any other HDMI cable before?
2. Have you tried resetting the video output from the XBOX?
"It can end up trying to output the wrong signal, so you can't see anything or get a flickering screen. Fortunately, there's a fairly simple fix if this happens. Remove any discs from the tray and turn the thing off. Then turn it on using a gamepad. As it boots, hold down the Y button, then hit and hold the right trigger. The video settings will reset to default, and you'll stop your sobbing."
Found on techradar.com