Okay, well, so much for an easy answer - or at least, that easy answer. It's possible that QTParted stole some of your /home directory to make the new partitions, but it's supposed to be pretty safe.

I think the next thing I'd do is check to make sure your user space is still okay, which would narrow down the possibilities to just losing some setting that affects X or KDE, probably.

Try starting Knoppix in console (non-GUI) mode with the boot parameter (cheatcode) 2. That puts it in run-level 2 instead of the default 5, which is where KDE gets started up automatically.

Log in as user instead of root and look around your home directory. In particular, see what configuration files you have. These are normally hidden by having names that start with a period, so the default ls command doesn't display them.
Code:
$ ls -d .*
The -d option keeps ls from showing the contents of directories.

-- Ed