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.
Supermicro 4U 36 Bay Storage Server 2.4Ghz 8-C 128GB 1x1280W Rails TrueNAS ZFS
$712.98
DELL PowerEdge R730XD 24x 2.5" Server Dual 750W Dual Heatsink - BareBones TESTED
$269.99
Dell Poweredge R640 Server | 2x Xeon Gold 6132 | 128GB | H730P | 8x HDD Trays
$1849.00
HP ProLiant DL360 G9 Server | 2 x E5-2660V3 2.6Ghz | 64GB | 2 x 900GB SAS HDD
$339.00
Dell PowerEdge R620 Server 2x E5-2660 v1 2.2GHz 16 Cores 256GB RAM 2x 300GB HDD
$89.99
Dell PowerEdge R730XD 28 Core Server 2X Xeon E5-2680 V4 H730 128GB RAM No HDD
$389.99
Dell PowerEdge R720 Server - 2x8c CPU,256Gb RAM, 128Gb SSD/3x900Gb SAS, Proxmox
$340.00
HP Proliant DL360 Gen9 28 Core SFF Server 2X E5-2680 V4 16GB RAM P440ar No HDD
$196.95
DELL PowerEdge R730 Server 2x E5-2680v4 2.4GHz =28 Cores 32GB H730 4xRJ45
$284.00
Dell PowerEdge R620 Server 2x E5-2650 V2 = 16 Cores H710P 128GB RAM 2x 600GB SAS
$274.99