kdm has been depreciated in favor of sddm it’s still there for LEAP not sure about TW it might not be compiled (search,opensuse.org is down I can’t check)
did you remove all 3rd party repo’s
what you are describing sounds like a graphic card issue what card do you have if nvidia/ati did you remove the 13.x driver?
tell us your repo list
zypper lr -d
you can still use the ncurses version of yast under console mode
if you have gpm installed you can even use your mouse
if not install it
zypper in gpm