It may not be to your liking, but here is what I would have done:

1. Get Knoppix 6.2.1, burn to CD.
2. Set it up on a USB stick on a CD-bootable computer.
3. Start Knoppix on the troubled PC in either of two ways: If it boots from USB stick, just use that, otherwise boot from the CD, and run from the stick. (Turn off any booting from the HD.)
4. The important command here is: At the boot prompt, write
Code:
knoppix fromhd=/dev/sdb1
or whatever the stick will be called. If the hard disk is called /dev/hda, it may be /dev/sda1.
Then you will get Knoppix to ignore the hard disk during booting, and you can mount it and do maintenance on it afterwards.

The fromhd= cheat code didn't work for me in 6.0.1, and 6.2.1 is way better anyway. Except for monitor detection and automatic screen resolution adjustment. With 6.2.1 you may have to use the cheat code screen=1920x1080 (or whatever the monitor does).

I routinely copy the KNOPPIX structure to hard disk, manually, boot from a stick/CD and run from the hard disk. That gives me full control over the Knoppix setup - and my experience is that I can't do with less.

Edit 20100219:
When run from disk, Knoppix 6.X shall be reasonable fast and efficient. If it isn't, there is probably something wrong. But beware of disk full on persistent images. That may give a hang without any notifications, in my experience.
So far, I have also good experience with setting up GRUB to load Knoppix (se my post in News). But I'm not sure how safe that method is if you are not somewhat used to low-level Unix things. It is easy to get something wrong if you don't know fairly well what you are doing.