There are remedies
I meant to check whether clamav is currently included in free Knoppix, forgot... you do get it in also free System Rescue CD, but I've got nervous about that. I also don't remember if I tested it on NTFS alternate data streams, which can be enabled in Linux but usually aren't by default. You'd want to use clamav with the most up-to-date virus signature file because your malware infection is probably updated regularly too with the latest word in nastiness.
I don't have a lot of knowledge about using the Windows CD or DVD to boot and clean up your computer, mainly because my computer didn't come with one, but it can be done. There are several free and respectable programs to protect your computer in various ways, such as Malwarebytes, most of which are not complete solutions in one. Choosing these is a matter of judgment. Your malware probably knows about all of these and will try to disable them and also hide from them. Also, this is where we started, there is malware around that poses as protection software products or pretends to be a similar product.
You also can buy a subscription to a security product such as F-Secure, covering several computers in one home at a reasonable price, but even this may be less effective when your computer is already messed up.
If your computer is wrecked, then backing up your data and then re-installing Windows from the original CD may be your best move - or even buying a new computer if it's time to do that.
If you jdon't have a Windows CD, don't buy a cheap bootleg - they are produced by the malware publishers. What I prefer to do anyway is to partition a Windows PC hard disk to have a relatively small system volume containing Windows and applications, that I can conveniently back up and then restore if necessary to repair my computer. Of course you start by making a backup BEFORE any partitioning.