Check out the Alix series SBCs (Score 1)

Pretty decent system for 5 watts; runs on a Geode so you can run most any x86 Linux distro. There's a slightly modified version of Ubuntu for flash filesystem, although if you're talking about NFS you'll probably want to add a disk. Limited support for that, but you can always use Passports or something like that via USB if you need multiple disks.

They make great routers, firewalls etc. in the diskless configuration. About $150 for a board, case and power supply, as I recall. NFS performance ain't gonna be great, but it should do it. And they run on 12 +/- a bunch volts, which make battery backup a real breeze.

For a little more power (in both respects) check out some of the older pizza box workstations or PC rack servers, like the HP 9000/710 or the IBM x300. Depending on processor and number of disks these things can be pretty frugal; getting into the 30 W range should be possible.