The more I think about this, the more I think buying a small PC might be the most robust answer. And not very expensive, considering the cost of PC's on the used market. I'm going to look into getting a smallish form factor, low power consumption PC, with a second hard drive for the media which can be slept when not in use. I might even look into running the OS off a flash card to save power. (A Mac Mini would work too, but frankly I can build a little PC for much less.)
I'm very interested in checking out TVersity for the media server stuff.