Forgot to cd /; sudo tar zxvf /path/to/AMD-APP-SDK-2.4/icd-registration.tgz?
Nope, didn't forget. Nothing I read anywhere said I had to do that. So I did, and now I'm back where I started: as soon as I start DiabloMiner I'm booted out of my login session.
You know how at the top of this thread you say that Ubuntu doesn't work? I think you need to mention Debian as well. I guess that makes sense - Ubuntu is a derivative of Debian, after all.
So, now it's time to reformat and install Windoze, and see if that goes any better.