I think that solves the problem, though I need to test it more fully. That's how I originally had it hooked up because at first I didn't have an HDMI cable. And I don't think there was a problem. I certainly didn't notice anything until I switched to HDMI.
Thing I don't get is, the TV has 9 inputs and the cable box has 4 outputs. In each case, the HDMI is just one. And yet having it connected affects everything else. Just seems wrong to me.
Assuming my cable box doesn't output 1080p (which is only available on the TV via HDMI), do I suffer any loss of quality by switching back to component?