http://pcpartpicker.com/p/3LJpq
AMD 3850 1.3GHz Quad-Core Processor
MSI AM1I Mini ITX AM1 Motherboard
Kingston Blu 4GB (1 x 4GB) DDR3-1600 Memory
Western Digital Caviar Blue 80GB 3.5" 7200RPM Internal Hard Drive
and some $20 or $30 mini itx power supply
And an old NES case for the case.
It would be less than $180 all said and done. Its a slow processor, but I figure since video encoding is usually multi-threaded the 4 cores would make up for that and it uses the same architecture the consoles use. Obviously it wouldn't be something usable for super competitive gaming like the new UT game when it comes out, it would be more of a "I don't feel like going to my room to play arkham origins" or something that works best on a controller.
Never really thought about a steam box until now with stuff being so cheap but I figured if any place would know something it would be here.