OK, sorry I pointed you to a very general documentation. But I had (and continue to have) good intentions, honestly. It seemed to me that you are applying the Slackware methods to your Debian system and this can only produce a terrible mess. Debian has much more refined ways of doing things, just like APT is infinitely more refined than Swaret (which works fine in Slackware, though). It seemed to me that if I pointed you to a document that explained some Debian basics, this would give you a good start.
I still think you should give this document, called Debian Reference, a second look.
You are not expected to read everything in one go. Rather, browse it and have a quick glance at any topic that seems interesting. It's also useful to bookmark this document, because it really is a rather good introduction into Debian and if you cannot find answers to your Debian-related questions elsewhere, you'll probably find them by studying this document a bit closer.
But you wanted more precise advices. I think you are correct in saying that you should log out of X before trying to upgrade your system. At least, you should log out of KDE before you attempt to upgrade KDE. The Debian tool that allows you to control services is called "update-rc.d". There are many other similar Debian-specific tools that you should use in Debian instead of the Slackware methods. The Debian Reference I pointed out introduces most of these tools. There's also an ncurses frontend for update-rc.d, but you should learn also how to use update-rc.d without this frontend.
So my precise advice is, do this:
# apt-get install rcconf
Then uncheck gdm in the rcconf program. Then reboot.
After this you should be able to log into console without starting X first.
Then su to root, do "nano /etc/apt/sources.list" and add these two lines:
testing main contrib non-free
testing main contrib non-free
Also comment out other lines you may have in sources.list so that these added lines are the only ones that don't begin with the character #. The "testing" in these lines refers to Sarge -- Woody would be "stable" and Sid would be "unstable".
After you've written the sources.list, you can do:
# apt-get update
# apt-get dist-upgrade
and if there's problems, you can try to fix them by doing:
# apt-get -f install
In general, your upgrades will be more successful if you initially make just a minimal installation, then do upgrade, and only after your base system is up-to-date you should start installing additional programs. Upgrading from Woody to Sarge and from Sarge to Sid are often successful (especially with the minimal initial installation) but downgrading from Sid to Sarge or from Sarge to Woody is likely to break your system.
BTW, you should know that when you install new applications, apt-get only installs the dependencies that your applications won't run without. But apt-get won't install the additionally "recommended" or "suggested" dependencies, although it is often wise to follow these recommendations and suggestions. The smarter frontends for apt-get are Aptitude (for console) and Synaptic (for X sessions) and they default to installing also the recommended dependencies, so you should use these programs to install any new applications.
Hope this helps -- and I still think you should read the Debian Reference and learn to do things the Debian way.
PS. If this upgrading business just doesn't seem to work, you might want to give the new Sarge Debian-installer a try before deciding that you've had enough of Debian.
It's still beta but if it works for you, you'll get a pretty much up-to-date Sarge system to start with.