As root, do
This will tell you if you have an IP, and how suse calls your eth card, which most likely will be eth0.
If you donīt have an IP, try
and see if it grabs an IP.
If you already have one, try to ping google (18.104.22.168)
First with the name:
If you can ping google by the name, you are set. If not, try with the IP:
If you can ping google by the IP but not by the name, you need a DNS server set up.
Good luck, and keep us posted.