My HDTV has only 1 component input (Samsung LNS3251D), which is used by the cable box. It has 2xHDMI inputs and a VGA port (plus various other non-HD inputs). I thought I should be able to use the VGA ...
If you can get 1080p on Component (basically go to settings->Display and select 1080p) you should be OK. If not, you need the VGA cable to get 1080p. You could set your 360 to 720p or 1080i until then ...