A friend got a 'glitched' xbox 360 and when connected with HDMI, it doesnt seem to work, meaning it boots but it doesnt do that circle light flash before going into dash, doesnt show any video. It works fine with component cable
You could clean the contacts on the HDMI port itself.
Otherwise it's a fault with either the HANA or worst the GPU (but that would probably cause an RRoD)
It's either that or live with it and use component cables (or the standart AV pack)
Since that does work...
chances are the glitch hack was bodged, the hardest point to solder is next to the hana chip and causes the most problems when installing. (although there's alternatives now)