Straight after a Slackware installation, you always boot up into a command line.
What you could try with your user, or with root: Execute
and then choose a window manager/desktop environment of your choice. If KDE doesn't work for you, try XFCE or any other. Then startx
If that works, you can edit the file /etc/inittab, so that the line that previously read:
That way, the system will always boot up into the graphical environment that you have chosen.