In regards to the HDCP, does that mean I would have to find some sort of capture card that was HDCP compliant? Is that possible? I hadn't thought of licensing issues being a factor. If its that much of a pain, maybe I will just have to suck it up and lose a monitor by routing the satellite signal directly into the monitor when I want to watch TV.
For HDCP to work, the whole path must be protected and it needs to be digital. The card, OS, and screen needs to be HDCP capable and can passthrough the handshake.
Why not only connect it to one of your screens? Its much easier that way. You can use the input button to switch signal between work and viewing, and since the audio is on regardless if the screen is, you can still listen to radio while working on that screen.