On OpenSUSE one can issue the command "rcxdm status".
It will tell you weather the X Display Manager is running.
It's output is similar to the following if xdm is running ok. (Notice the text "running" to the right).
Code:
Checking for service xdm: running
xdm.service - LSB: X Display Manager
Loaded: loaded (/etc/init.d/xdm)
Active: active (running) since Tue 2015-07-21 22:12:37 CEST; 1 weeks 5 days ago
CGroup: /system.slice/xdm.service
├─4213 /usr/bin/xdm
├─4215 /usr/bin/X -br vt7 -auth /var/lib/xdm/authdir/authfiles/A:0-V*****
├─4230 -:0
└─4286 /usr/bin/xconsole -notify -nostdin -verbose -exitOnFail
If it says that xdm is "unused" of "failed", then you may get a clue as to what is wrong.
The text "active (running)" means the service is
active and thus will be started after boot, and
running means it is currently running.
One thing to attempt is running "rcxdm restart" or "rcxdm start" to see if it will run and present you with a "gui" to log on to. If it runs after starting it manually, then the service isn't activated properly, or the system booted into the wrong (non graphical) runlevel, as mentioned above.
There is more to this. What version OpenSUSE do you use? How did you install it? Using textmode or graphical installer? Has it been running in gui mode before? Have you changed graphics adapter? Have you updated the graphics driver recently? Have you made any changes to the boot settings before this happened?