Ummmm... no - sounds like you are being screwed.
YOU need to do some work here - some basic testing.
1. Start unhooking the component cables from your TV one by one. Unplug it, see if there is an image change, then plug it back in. My guess, is that only ONE cable will appear to work.
2. The cable that works - likely the bottom most cable out of the back of your cable box (the green one?) is probably the one... Plug it into the composite input on your TV and see what happens. Turn your TV to that input!
My guess is that you have something like the Explorer 8000HD cable box and it is not set to output HD video content. It is set to output composite. This means that you aren't getting anything worthwhile out of your cable box right now. Just the same piss-poor garbage that has been around for years. Not what you want.
So, you must go through the owners manual for your cable box and set up the component output of the box to actually output component video - likely at 1080i fixed. This should be covered in detail in your manual.
Don't spend one more cent without first finding out if it is a cable issue vs. a TV issue. Transcoders generally take video from one format to anther - like s-video to component video. This completely defeats the idea of you having HD component video direct from the box!
Give it a try - get back to us - give us a specific TV model number and a specific cable box model number and your cable provider name. Make sure, if nothing works, you test the cables as well.