Now here's a funny thing!
I changed my 3rd IDE hard drive to a larger one, and Knoppix now 'sees' it. The evident difference is that :-

* The original was 6.8 GB (< 8GB) and was managed by the BIOS in NORMAL Mode. For this disk, Red Hat or Mandrake fdisk reported the Extended partition type as "Id: 5, System: Extended". This was the disk that Knoppix did not 'see'.

* The new disk is 40GB, and is managed by the BIOS in LBA Mode(like my hda and hdb). Knoppix 'sees' this disk, and Knoppix (and Red Hat etc) fdisk report the Extended partition type as "Id: f, System: Win95 Ext'd (LBA)"

This is not directly an explanation, but it may provide a CLUE to anybody who has deeper knowledge, than myself, of the system!
Any explanation would be interesting; meanwhile I'm happy that I can now use Knoppix system-wide .