To save your old environment you have to put /home on a different partition. To do this copy /home over:
cp -Rpf /home /mnt/hda#
where # is the partition number.

Then just reinstall Knoppix. Then to get your old environment working with the new install go to the text file /etc/fstab. Add the line
/dev/hda# /home your_file_system defaults 0 0
Changing # and your_file_system to the correct values.

This method will still requier reinstalling individual programs but the configuration files for those programs will still be set up in your /home.