Hi, Pete. Is that cable box a rental, or do you own it? I'm asking because I'm wondering if you can get your cable company to upgrade your box to one with HDMI. If it's a rental, they certainly should. That could help simplify the connections a bit.
You can set it up so that you can watch TV without turning the receiver on. You can have one set of audio/video outputs from the cable box running to the receiver, and a second set running from the cable box to the TV. That wouldn't be a problem because your TV will accept multiple video inputs (one from your receiver, and another from the cable box). There might be an easier way, but from I see on that cable box, I think that a splitter for the component video might be best. You would run the optical audio from the cable box to the receiver as you have it, and run analog audio from the cable box to your TV.