You've got the cable box configured correctly--it should be outputting 1080i only (uncheck the rest of the resolution options).
On the TV, you haven't been trying to output sound from the TV to the receiver, are you? I ask because AV4 is the input that's used with the Audio Return Channel on this receiver.
For the receiver, I'd do a factory reset to clear out any SCENE settings that you might have made while troubleshooting. Next, go into the settings and disable HDMI Control. Both of these are in your manual.
After that, for troubleshooting purposes, forget about using the SCENE button on the remote (the white TV button). Just turn the receiver on, switch to the HDMI input where your cable box is connected, then turn the cable box on, then the TV.
Does that work?