zvacet.
This sounds familiar to what you are experiencing. You could try the solution by zorael and edit the /etc/X11/kdm/kdmrc.
First make a backup of file /etc/X11/kdm/kdmrc and save it somewhere in case it does not work.
Open krunner (ALT + F2) enter
kdesu kate /etc/X11/kdm/kdmrc
enter root password
Then in editor, add to section:
[X-:*-Core]
AllowNullPasswd=true
AllowShutdown=All
NoPassEnable=false
NoPassUsers=
ServerArgsLocal=-nolisten tcp
ServerCmd=/usr/bin/X
TerminateServer=true
save.
Probably better error logs would be kdm or xsession since it is a display problem. Looking further into it to see if I can find some similar problem that has been solved (read somewhere it could have to do with hibernation or screensaver). If it works, post it to the bug report.