If "eth0" shows up in the ifconfig listing, then a driver has been loaded, however it may not be working. From a quick Google search, your computer looks like a pretty new model. The version of the Linux kernal included in DSL is pretty old, some more modern hardware drivers aren't included with it.
Look up the chipset of your computer's motherboard and search for when Linux driver software was developed for it. You might be able to load the drivers as modules on startup, but that relies on them supporting the linux Kernel version used (2.4.31).
If the support isn't available, you might want to try DSL-N which uses the 2.6 kernel. Or you could wait for John to release his promised new version of DSL that sounds much like a new DSL-N, supporting newer hardware but bloating the distro somewhat in terms of size and resource usage.
I tried this but it didn't work for me. Anything else you can add to this? Thanks.