So I have a Coax cable coming from my satellite that carries compressed HD A/V (audio being only 5.1). But I need to uncompress it to make it usable. So before the sat receiver, the coax is carrying a signal capable of eventually being HD, but not until it is uncompressed.
You kind of get it... The antenna points at the sky and gets signals from the satellites. Some of the signals are 480i, some are 1080i, some may be 720p, and some may even be 1080p. But, they are all scrambled together and mixed up, you need a satellite receiver box to make sense of this jumble and spit out ONE channel to watch.
Once the signal is uncompressed, it can only carry crappy 480i. Is this correct?
This is where you are most confused...
If you have a HD satellite receiver box, then it will decode, for example, HBO-HD, and can output HBO-HD over one of the HD connectors on the back of the box. These HD connectors will include component video and HDMI video output. If the box has s-video out, composite video out, or a coaxial out video connection, then the best video quality will be 480i, and it won't touch the other types of connections.
Use HDMI if you can... otherwise, use component video.
It sounds like the Sat Box receiver is the weak link.
If your satellite box is not a HD version, then it is definitely the weak link. You have zero HD capability without a HD satellite box.
Once it is uncompressed, could I use another device to make the signal better?
Yes, but it would only be marginally better, and it would be far less expensive to simply get a HD satellite box.
So with my current non-HD receiver, only putting out 480i, could I put another device between the sat receiver and my TV and boost the signal.
It's actually called upconversion, scaling, or video processing, and the answer is 'yes' as it is above, but the improvement would be marginal, and pricey.
This is more hypothetical, as I know the solution is just to buy a HD receiver. Just curious what happens to the extra uncompressed material. Is it lost forever once it goes through the sat receiver?
No, a non-HD sat receiver can't decode HBO-HD or the other HD channels at all. Sat receivers use their tuner to descramble and decompress ONE channel at a time. They could potentially try to decode HBO-HD, but they don't have the horsepower to do so fully, so they would fail at the process. Instead, you could get standard HBO from the box.
If you list the actual model number on the back of your satellite box, and what service you have, you can even get a more specific answer as to what you need to buy.