You didn't say what version of Knoppix you are using. If it is anything but the most recent version then memtest should be there. If it is the newest version, well I have not downloaded that myself; a lot of useful stuff has been vanishing from Knoppix but removing memtest seems like a really bad idea if that happened. memtest needs to be typed in all lower case, just in case that was what went wrong.

Knoppix should be able to see the hard drive even if the boot sector is infected, although it may take some experience with Linux, particularly with newer versions that removed the desktop icons for the partitions. And it should be able to write to the disk (although writing to NTFS partitions may corrupt them and is generally made difficult for that reason). Of course, a failed drive might not be accessible.

I'm hard pressed to believe that you picked up an infection just when the disk died, and you certainly didn't pick one up after the disk died. So if there is a hardware failure that is the problem and if you also have a MBR infection then you likely have for some time and have been living with it. But as I said, I think more people cry infection when thee isn't than really have a speculated but unknown infection.

In addition to the suggestions that I already made, you might learn more just by looking at your BIOS. A BIOS can report a drive even if it failed, for example if it isn't spinning but the electronics are working. But if it is no longer showing up in the BIOS a drive's electronics have likely failed (or you have an interface problem or a connection problem).

Good luck. I still think the best idea is to swap in a different drive, better understand what the issue is, and rework the old drive as a second drive under Windows if the hardware is OK.