Really? No ethernet?
You have two versions of the A13 OLinuXino, one with WiFi and one without. Both of these have 4 USB ports available and Olimex sells USB Ethernet dongles. I have A13 OLinuXino with WiFi and with the USB Eth dongle, both thw WiFi and Eth work perfectly. I'm running Debian on it at the moment but I'm also preparing Fedora for it.