If you can figure out the changes you made to KDE, then maybe we could get down to what went wrong, and how to undo it. Did you edit the KDE menu entries for OO and Iceweasel?

The command for Iceweasel is 'iceweasel %u'
The command for OOo is 'soffice private:factory/swriter'

I went in to edit Iceweasel and OOo at the same time - bad move! I tried opening OOo and nothing happened. I tried again and it seemed that my machine froze. I rebooted and things were ok. I was able to run both the weasel and office. Try the commands above and let me know what happens.

You wrote:
When I boot with home, then things start to fall apart. Like I said OOo does not start up at all (but it certainly does try for a very long time); if I try to run Weasel (whatever the FF replacement is called), then I actually get an error from KDE, something about the KDE launcher not able to find the executable or some such.
I almost suspect an issue with KDE not Knoppix, however, I have no idea how to proceed to figure out what happened.