Many Ethernet cards do not function "out of the box" with the liveCD, essentially because their driver require some piece of non-free firmware.
The Broadcom Gigabite Ethernet cards for example require the tg3 driver, that includes such "binary blob". But actually, the card can work without it, although since nobody knows what this non-free firmware does, it's hard to tell why or *how good*.
The Linux-libre project releases freed kernel sources, that is, freed from these "blobs", and it is sometimes possible to compile them including the required drivers in order to benefit the use of some hardware, even if only partial support is provided.
You can also check out Ali Gündüz' builds, that are trying to get most of Ethernet and sound cards working, and even numerous wifi chips. The 2.6.29.x builds do not support suspend/resume on the tested hardware (Lenovo Thinkpads and Acer Aspires), so we would advise to grab the 2.6.28.x version.
The easiest way is to boot off an Ubuntu or Fedora liveCD, since these distributions are shipped with Linux kernels containing the non-free firmwares that are removed from the one gNewSense ships with. Go to Ali Gündüz' website, download the linux-headers and linux-image .debs and save them on you hardrive. Boot into gNewSense, and just double-click the files : the installation programm will do the rest. Reboot and enjoy. You can even download the tools from there on to recompile your own custom freed Linux kernel.