Happened to me too the other night.
The consoles case was off when I plugged the HDMI cable in. TV was on at the time, and the Xbox 360 was off.
I saw 2 tiny sparks come from the end of the HDMI cable when I accidentally touched it to the metal case.
Standard definition cable seems to work, HDMI not at all. The same cable + TV both work with a different console though.
No clue how to go about fixing it.