You are not seeing chomp errors during the Knoppix boot are you ? Some of the symptoms you describe sound like a dud CD Drive.
The Knoppix thing sounds like X cannot talk to your graphics card, you may want to use some of the boot options to force Vesa mode (you will still have KDE but it will be a little slow).
Another very likely possibility is dud ram, Ram can go in funny ways (including being triggered by temp or just being intermittent) So my advice is to use your other box to burn a Memtest86 Boot CD and run it overnight, checking for errors in the morning.
www.memtest86.com
If CD burning isn't an option you can also find Memtest on some Linux installation media as a pre installation boot option (SuSE and I think Ubuntu does this)