The processor and GUI have little to do with one another. If Knoppix fails to load a GUI, then the problem isn't the processor but the video card. It may be new, or have some strange issue with the knoppix CD. Any 32 bit distro should run on a 64 bit processor, it just won't take advantage of the 64 bit capabilities. You can try several things -
1) try the newest Knoppix, which is 3.8 I believe from knoppix
That may have the correct drivers for your video card.
2) If that fails, try another live CD. Almost all of the distros now have live CDs now. I know both ubuntu and kubuntu have 64 bit live CDs, but any other distro may be fine.
3) You could get a 64 bit version of knoppix, which isn't official, but a community effort. It looks like it is a 64 bit port of knoppix 3.4, so if 3.7 doesn't recognize your video card, the chances of 3.4 recognizing it aren't great, but it may be worth a shot. Check it out here