Well, I'm no expert in this area, but I do know that the C3 is a socket 370 design so that means it will have to be a board capable of running Intel processors. I doubt that the Intel 810e/815e chipset would run it, but I know that Via chipsets run it. That little silver Shuttle computer that everyone keeps talking about (AV24 I think??) uses some sort of Via chipset and I believe I've read reviews with it running a Cyrix processor.
I know this isn't much help but hopefully it will point you in the right direction. Also, I don't know of any fanless Power Supplys, but someone here posted a FAQ on how to make an Antec power supply silent by removing the fan in the back and inserting a silent one (I'd imagine that this mod would work on any kind of power supply and not just Antec).
Hope this helps at least a little bit.