Linux won't know that you're DSL. DSL/Cable modems look like just one more ethernet connection.
What you need to look at is whether your Ethernet card is up.
Do (as root) "ifconfig". You should see one that says "lo0" that is your loopback (an internal memory-to-memory thing that is treated like a network device to make some other software simpler).
You should see another that says something like "eth0". If you have that, and it has an IP address, then your card is up, and you (probably) have a routing problem.
I don't know how ethernet cards are configured and started in Suse. You'll have to do some research on the Web to get that (or maybe you'll get lucky and somebody will know here).
The other possibility is that you have a routing problem.
I'm not going to try to describe everything that goes on in networking -- it's too big a subject. Here are the major things to look for:
Ethernet card is up (described above)
Ethernet card has an IP address (probably need pppOe or dhcpcd if it's up but doesn't have an address, and possibly if it won't come up.)
Gateway is defined (this is the "default" route when you enter the "route" command. Your ISP should tell you what it is.
Nameservers are defined in /etc/resolv.conf (Again, your ISP should tell you what they are.)
If you have an interface (the eth0 when you do "ifconfig"), try the following:
"ping 127.0.0.1" (the loopback) This should ALWAYS work. Something is seriously wrong if it doesn't.
"ping w.x.y.z" where w.x.y.z is the ip address of your ethernet card. If you can see an IP address when you run ifconfig, this should work.
"ping a.b.c.d", where a.b.c.d is the IP address of your gateway.
If it comes back "host not available" or "unable to access host", you have a routing problem.
I was going to go deeper into this, but I'm both in a lot of pain (very recent onset of carpal tunnel) and I'm realizing it's going to be really hard to explain how to fix this without knowing how Suse configures and starts their stuff. I can tell you what to do, but not how to do it on Suse.
I'm going to stop here and let you find out what you can. Post as much info from the commands as possible (I understand that with no network connection, you can't post from that machine, but do the best you can.)