I've had the same problem when trying to run the CD on a shuttle SK41G system - this is a small formfactor system with a ton of on-motherboard stuff. Many distros refuse to even boot on the thing. Knoppix does though, but not as well as I would like in the graphical login department.

The first thing to do is to switch from the blank screen to an alternate window. If the last line in the CTRL-ALT-F1 window is 'Starting X11...', and going to one of the others (CTRL-ALT-F2 for example) gives you a root prompt, then the problem is simply with X11. I've found two ways to force something to come up when booting from the CD.
  1. use the 'knoppix screen=640x480' cheatcode.
  2. On the blank graphical window (CTRL-ALT-F5 if you switched!), press CTRL-ALT-KEYPAD+. Depending on the modes enabled at bootup (you can see this in CTRL-ALT-F1), you might need to do this more than once, until you land on the 640x480 setting. I have never been able to get any other resolution to work. NOTE: When you use this method, you end up with a small physical window on a larger virtual one. It gives me a headache.

Since my intent all along was to do a hard-disk install anyway, I went through that, and my hard-disk image doesn't show the X window either. So, I took a peek at /etc/XF86Config-4, and after removing the DDC-detected HorizSync and VertRefresh settings and killing the X11 server, BANG! up comes graphical login in 640x480. I say this is a smoking gun on detected video problems. The odd thing is, knoppix *is* properly detecting the onboard video (Savage8 KM266). It just doesn't seem to want to work with anything other than lifeboat default sync rates.

Anyone have other ideas? I really don't want to abandon my attempt to get Knoppix working on this hardware - Knoppix in a toaster box is such a cool thing! PV