I have the SA explorer 4250HD cable box which is similar to yours but without the PVR and cable card connections so the menu set-up should be similar if not identical.The set-up you are striving for "does work" in my system so we will have to look at the detailed settings. Firstly, since you are using the receiver for all your sound, I am assuming you have disengaged the TV monitor's speakers.
Next, going in to the "settings" menu, ie. pressing the settings button twice to get the detailed set-up menu in which you scroll up and down the left-hand side, check the digital audio out setting (it will show HDMI, Dolby Digital or other) confirm it is set to Dolby Digital NOT HDMI. In addition, your picture format setting (which should show Auto DVI, upconvert 1 and 2 and fixed) should be set to upconvert since that setting deals best with non-HD programming. 1080i HD channels will pass through as normal. Remember with any of these settings, you must press the "A" button to lock them in. As you notice when you plug in the HDMI cable for video it overrides any other video input. Obviously, the problem is with the audio and I am at a loss to explain why the TV would be affecting your cable boxes audio configuration. It doesn't make sense. HDCP generally only applies to the video and not the audio. There are many set-ups out there in which individuals have both HDMI video(out to a monitor) and coax or optical connections plugged through a receiver at the same time so the television shouldn't be affecting any of this.
At any, rate, see what your detailed connection set-up is currently reading and we'll see what happens and take it from there. This shouldn't be that complicated!!
