Okay I understand mostly where you're coming from - the only thing I don't understand is the Cable that provides HD content (because I don't have cable - never seen it in use - will have to research it). I was specifically asking for this, because we may need to ensure that your motherboard has a certain port that you can plug the Cable in to - this is why I was asking how do you currently display your HD content? Are you aware of the name of the port/plugs that your Cable uses (that would be plugged into the computer)? Somebody else may need to help out here...
On to the parts themselves, though, I strongly suggest you start by finding a mATX case that fits in your available space. Currently, here
is a list of Newegg's HTPC cases, and here
are the slim mATX cases. I personally like that Antec slim mATX case, as they make good PSU's, and this one is an 80PLUS certified unit (high efficiency). I would think that 350W should be enough for this build, but we'll double check that once all the parts are chosen.
A low-end ATI video card will be a good choice here, as they are able to process the HD content onboard, minimising use of the CPU. The HD3450 series are good and cheap, and you can get ones with passive heatsinks for silence.
Do you have a specific budget to stick to here, or just to get something that ticks all the boxes for your uses?