Nobody has answered you so far, it might be worthwhile to think about why..

Zeroth, if problems are only with graphics, you could try to run Knoppix without graphics. Check out the init runlevel stuff. You can do all necessary administrative tasks from the command line.

First, I think you illustrate why I personally try to avoid ordinary HDD installs of Knoppix as much as possible. Running it the ordinary way and making regular backups of the persistent storage (knoppix-data.img) is IMHO far easier and safer. Accessing knoppix-data.img outside of Knoppix is mostly a matter of simple loop-mounting (ignoring the unionfs markup).

Second, if you have booting problems with a PC (trouble getting anything to run) and want to access the hard disk, the Safe And Simple Way is to take the HDD out and mount it in an external (USB2 will usually work just fine) cabinet.

Third, driver problems are, generally, an upgrade indication. Not always, some times we have to downgrade, but my advice is that you try to attack this problem with 7.0.4. The nouveau stuff may have developed a lot since 6.4.3, I guess.