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This machine has no internal hard disk, only an external USB drive?

You didn't tell us the output of "blkid" and "fdisk -l" and you didn't tell us the error messages while trying to boot with the...

You can create a Knoppix boot-CD or download a bootonly CD from the Knoppix mirrors.

What you want to install is the "Poor man's install" as I described it at
http://knoppix.net/wiki/Category:Hard_drive_Installation
and I never heard from other peoples about problems using an USB...

'Are you sure, your external drive is '/dev/sda' and the partition is '/dev/sda1'? Please boot Knoppix again without the cheatcode "tohd=/dev/sda1" an tell us the output from
blkidand
fdisk -l