I'm running a dual core ATOM fanless desktop with a Squeezebox Touch. Very happy, including streaming hi-res.
You can see configurations like it at
http://tranquilpc.co.uk ; They also have some newer i3 and i5 based systems.
Try also
http://endpcnoise.com. They have some configurations that would be right up your alley, but maybe more powerful/expensive than what you want. In any case, the site is good for finding out about quiet/silent components. They will also answer email/phone questions.
You don't have to get a USB DAC. You can also use something like one of the quality USB converters from M2Tech or Empirical Audio. Also note that on some DACs (even good ones), the USB implementation is either not very good sounding, or limited to lower resolutions, or both. Check before you buy.
The Nova is a very good solution if you don't need a high powered amp (or just use it as pre/DAC).
Fanless/SILENT is good, but adds cost. If you want just a quiet PC, usually upgrading to a quiet motherboard fan and quiet case/Power supply fans (under 25db) will do most of what you need so that it isn't bothersome. Outfitting an inexpensive PC this way would only add $100-$150 to the cost, yet make it much quieter than a typical configuration, even for a fairly powerful PC. Note also that some of the nettop or small standard PCs are fairly quiet out of the box, as all their components are on board (fewer fans) and they have external PS.
If you use an NAS box to stream, just make sure it is powerful enough to run any software you want and stream successfully. Some NAS's are mainly for storage, and don't stream so well. Lots of info at various forums about which NAS boxes are good streamers. Also, if you run both USB storage and USB DAC there can be some SQ issues, as the USB demands are too great for top quality audio results.
Also, most MacMini users report that the Mini is quiet enough that it doesn't bother them, for instance.