Hi, guys - I'm b-a-a-a-ck; Ethernet is working now, using the new driver. I decided to write up the steps I had to use to get it working, so someone else with this problem can stop beating his head on the mousepad.

This is a necessary step for THIS motherboard. ifconfig shows an IP and everything looks normal but it simply will NOT work with the kernel-supplied r8169 driver, and the SUSE driver repository has only archaic versions.

Steps in "what worked":

1. Download the openSUSE 13.1 install-DVD using another PC:

2. Go to the official Realtek download page for the Linux/Unix Driver for the RTL8111/RTL8168 ethernet card and download the latest driver version.

3. Load the downloaded driver file to a USB stick

4. Install openSUSE 13.1 from the install-DVD

5. Set the 13.1 install-DVD as a repository in Yast

6. Install zypper from Yast

7. Get kernel headers & build tools from the install-DVD:
zypper in -t pattern devel_basis devel_C_C++ devel_kernel
8. Copy the downloaded driver file from the PC-loaded USB stick to the Suse box
9. Untar (decompress) the archive:
The driver is in a compressed archive. Decompress it with the following command:
tar xfvj r8168-8.037.00.tar.bz2
Note: Remember to replace the “r8168-8.037.00.tar.bz2” with the driver version you have downloaded!

10. Blacklist the old driver:

Some systems may need loading of the old driver prevented and others may need both drivers available. To blacklist the old one, set a new entry in /etc/modprobe.d/99-local.conf:
blacklist r8169
OR enter in the terminal to do this in only one command:
echo “blacklist r8169” >> /etc/modprobe.d/99-local.conf
11. Build and install the new driver:
Change to the directory containing the newly downloaded and decompressed driver - from:
 /home/whoever/Downloads # cd r8168-8.037.00
 /home/whoever/Downloads/r8168-8.037.00 # 
Note: Again, remember to change the “r8168-8.037.00” to the newly downloaded version.
Build the driver:
/home/whoever/Downloads/r8168-8.037.00 # make clean modules
Install it:
/home/whoever/Downloads/r8168-8.037.00 # make install
12. Welcome r8168:
Let the system know about the r8168 driver. Rebuild the kernel module dependencies:
/home/whoever/Downloads/r8168-8.037.00 # depmod -a
13. type “exit” & [enter] two times to close the terminal.
14. Remove the openSUSE 13.1 install-DVD from Yast/Software Repositories.

Thankyous to Czeslaw and Knurpht and all the other Obi Wans....