Alright, well there are three likely reasons this could happen. Let's check for them, and see if we can fix your problem. Here are the possible problems:
- The problem is with your HDMI cable. The end(s) may be bent out of shape, which could prevent it from working correctly. Try using a different HDMI cable with your xbox and TV -- if this fixes your problem, then you had a broken HDMI cable.
- The problem is with your TV's HDMI port. To check for this, hook something else up to the HDMI port in your TV. In other words, connect a DVD player, Blu-ray player, or anything else with HDMI output to your TV and see if it works. If other devices work, then you know your problem is not with your TV.
- The problem is with your Xbox 360's HDMI port. If you've tried the other two tests above, but your HDMI cable and TV's port work just fine, your Xbox 360 may have a damaged HDMI port. If this is the case, you should contact xbox support via chat or phone, because they can repair your Xbox for you. You can contact them from this page: support.xbox.com/.../contact-us
The good news is, your xbox is working just fine, apart from the hdmi display, since you can use component to play mostly normally. I hope this helps! Good luck getting your HDMI back on track.