I'm not saying it is this but my first thought is a cable fault and the second the TV. Have you checked what resolutions the TV supports through Component? Some do not like 480i and, if so, that's a problem.
If you set up the TSOP, softmod or whatever with a SD cable then whatever the default settings for HD are there is no way I know of to change them until you get a HD cable that works - a chicken and egg situation. AFAIK even though you can change the resolution settings using the UnleashX dash with a SD cable type fitted it doesn't save them. You could try doing that but I'm not hopeful. I'm also thinking that with Shadow C protection you'd need to turn that off first too.
You could check the cable if you have another Xbox and it causes the same problem but, of course, if it is the cable then there's really no solution other than to replace it.
This just occurred to me as it solved a problem I had where one Xbox which for some unaccountable reason was stuck in 1080i even when used with a SD cable. The trick you could try is the reverse of what I did and again requires the UnleashX dash and Shadow C protection, if used, disabled.
With a Composite cable go to the UnleashX System > Settings > Video Settings screen and alter the resolution settings to 480p/720p/1080i then, whilst still on that screen, hotswap from the Composite cable to the connected Component cable. No guarantees.
If somebody knows a simpler solution to a situation like this I'd be interested to know myself.