So many people have this type of problem and there seem to be a lot of different causes. When I had the problem the fix was as easy as switching it into recovery mode (which magically allowed there to be video) and putting on a newer version of the xenium OS. I've herd that with 1.6's you may have a video problem so the fix was to burn a copy of the new xenium OS and a dummy file onto a CD-RW or what ever media your xbox reads well. Switch the xenium into recovery mode, place the cd into your xbox, power it on and hope to see the leds flash red and orange and then power down, then switch it back into normal operating mode and try to boot up the xenium OS using the eject button and walla, you got picture.
No promises this will fix your prob. a lot of times it's a solder problem, or trace, or solder splash, good luck though.