I'd be tempted to build a PC anyway. In a typical modern PC, the typcial energy users are:

1) CPU. GHz+ processors are hungry. Good news - for file serving a couple hundred MHz is plenty. Use a low end P3 or higher end P2, and you'll cut this consumption to the point where passive cooling (ie no fan) is a possibility.

2) Graphics. Modern 3D cards are getting to be as powerful as the CPUs. Good news - you don't need it. Any built-in or cheap 2D capable card is enough to configure your beast, and if you're not running GFX intensive programs you won't use much power at all.

3) Hard Drives. hdparm is your friend. Set the spin down to a few minutes.

4) Power supply inefficiencies. Roughly proportional to outputted power. Since you won't be using much power the power wasted here isn't much either.

You should also look at embedded boards on ebay. The embedded world often has strict power requirements so you'll find other options, eg the NS Geode (basically a P2 MMX compatible CPU) that has low power requirements. Many are linux compatible, but you should do your research first. Beware that the board is often the easiest part to get - most of them use 0.1" IDC headers for nearly all their cabling so you'd need to source or make cables to connect a keyboard or other peripherals. Also beware of power supply requirements - they can usually be satisfied by a standard PC supply but you'll probably need to rewire it.