Is there a Free as in Freedom single board computer? I do not think so.
I usually design my PCBs using Fritzing which is free under the GPLv3. But I think you cannot use Fritzing to design a single board computer.
It might be possible to design a free as in freedom mobile Ogg Vorbis Player using Fritzing, the VS1000 - Ogg Vorbis Player System Circuit, and a charger for a LiPo bat.
Building an Ogg Vorbis player that meets the Respects Your Freedom hardware product certification might be possible, but I think that it can't be cheaper than an A13-OLinuXino.
Free as in Freedom hardware will cost less, if more people cared about freedom. The Letux 2804 smartphone which runs GNU/Linux costs about 800 EUR, because it is made in small batches of 100 units.
