You only need the TV to serve as a monitor. There is absolutely no reason to run sound to it or from it. All it needs is video. Turn the speakers on the TV off. That said, in order to get 1080p from your HD-DVD player, you need to run an HDMI cable from that to your television. It carries sound too, but that's insignificant because you won't need it for that. For audio from the HD-DVD player, you can run a digital optical cable or a digital coax cable from the HD-DVD player to the surround sound receiver.
For any source that is less than 1080p, including your HD satellite receiver (which does 1080i at best), you can connect both video and audio directly to the surround sound receiver. Use component (red/green/blue) cables for video and another optical or coax for audio. Same goes for a traditional DVD player, XBox, PS2, etc.
Now you can use the surround sound receiver to switch between sources. When set up correctly, when you switch from one source to the next it will switch both the audio (out through the speakers) and the video (palyed on the monitor). The exception is the HD-DVD video. You ran it directly from the HD-DVD player to the TV without going through the surround receiver, so you need to switch the input on the TV itself.
This is all assuming you have a surround sound receiverthat does not have HDMI inputs and outputs. If it's 6 months old or older, it likely does not. Even a lot of newer ones still don't have it yet.
If you DO have a surround receiver with HDMI inputs and outputs, you could potentially run every piece of equipment (assuming they have HDMI outputs) to the surround receiver with HDMI cables, and then run one HDMI cable from the receiver output to the TV input.
Just remember - treat your TV as a monitor only. Don't worry about getting sound to it or from it.