Interesting. I am having this exact problem with a DCT6200 attached via component to a 30" Philips HDTV. I have another DCT6200 in my bedroom on a standard definition Toshiba 20" FST PURE via S-video and CC works fine there. I am not sure about my 65" Mitsubishi HDTV downstairs, will have to try it.
Any known fix for this? The CC feature on the box settings is bad.