There is a distro called LinPVR which network boots a diskless computer of sorts into a MythTV frontend. It supports those diddy MiniITX motherboards and the like.

An old laptop with a busted screen from eBay could work well I'd expect. That would be small, quiet and also may have S-Video output.

Mac Mini would make a great Frontend. Not cheap, but works great and also has a remote control included.

The Original Xbox can be had really cheap these days. I am running XBMCMythTV which is a Frontend written in Python for XBMC. Watching Live TV does not work for me, and it is not quite perfect. The channel guide and setting things to record needs a bit of work (we use the web interface MythWeb for that, its great). Watching recordings works ok. XBMC clocks the fans down to a very quiet level. You can get the Xbox to boot Linux and have a proper MythTV frontend on it where everything will work, but that requires some more effort, booting time and I don't know whether you can control the normally loud fans. It is also big and ugly!