In my case there were two different selections on the TV's input menu that used the dual mode input jacks. (But wait, there's more.)
As you can imagine, my super cheap guy was using a cable box (free or cheapest available from Comcast) that had only Composite output. I used the yellow banded input and the TV's input menu presented an "A/V" input and displayed a better than expected stretched image or an image with matting bars on a 16:9 display. He was then complaining about the stretch or bars. At about this time I had noticed the detail that there were two sets of color stripes on those input jacks.
On the other side of the wall we had a full setup with a Plasma TV and a free set of Component outputs on the cable box. Since we already had a hole in the wall backing the two TV's I quickly pulled a Component cable through the hole to show what could happen if he wasn't so being so cheap.
This is where I bumped into the quirky dual use aspect of TV input jacks. As I recall, after the reconnect, the first time I went through the TV's Input menu, the Component input that I needed was not presented. This suggests that the TV attempted to second guess the signal type, if any. Similar to your experience, I struggled for a while with no picture. I don't recall exactly what transpired, but eventually a Component input was presented and things have been fine.
Perhaps the moral is -- read the directions -- wherever they are.
