When you do a full HD install, what you get is basically a functionally and mentally retarded Debian variant. That's why so many of us advice against it. I do a poor man's install instead, just using partitions on the HD (extrenal or internal) instead of CD/DVD/Flash. Then I get both the advantages of HD install (mostly) and of Knoppix. Booting is done either via GRUB or syslinux - setting up with GRUB is a less error-safe, but better overall solution IMHO. But to avoid any effects of a full HD install, I don't use that mechanism to install GRUB.
I have found that for general use, this solution works better for me than a full Debian install. YMMV - there are good efficiency and system administrative reasons to go the full Debian way, but I'm amazed at how little reason there is program-wise in Knoppix 6.X. And it only gets better.
If you do a poor man's install to an external USB HD, you can check that this works on another machine before trying out your problem baby computer. I would have gone the whole way, installing GRUB on the internal HD, setting it up to boot the external HD, checking that everything works properly. And then moved everything over, trying to boot the problem computer. Without graphics at first. If this doen't work, I would have tried if ANY Linux distro could be started, and if so, simply used that.
The HW detection/automatic setup does not work so flawlessly in the recent Knoppix versions as it used to. It has become much more versatile, but seemingly much more bug-laden too. Your Debian experience, could indicate that this may have to do not with Knoppix tweaks, but with upstream bugs.

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