Well, first off, if you don't need a high performance machine, you sure as heck don't need a quad-core CPU. The media PC at my place, which you've seen, has a very plain-vanilla single-core 32-bit Athlon XP in it, at least 3 years old, and that machine plays video just fine.
If you can go just a little larger than a Shuttle barebone on the chassis, 10.5"W x 7.75"H x 13"D
, I have one of these
I'd sell for $50
(used, good condition). Comes with 300W PFC power supply.
You'd need a mainboard (MicroATX size), a modest CPU (maybe dual-core) w/heatsink, some RAM to match the CPU and mainboard, hard drive, DVD drive, TV/video card(s), a quiet fan or two, keyboard/mouse, and operating system software (Linux with MythTV is free and do-able). You may also want to get a media remote, or upgrade to wireless
What would you be hooking this up to? TV, monitor, projector...?