Hi,
I don't think I'll be able to fix your problem due to noobness, just to tell you not to hope in advance
To me, it seems like some problem only occuring in 64bit mode, right? As it occurs with two distributions, there seems to be a distri-independent problem with the hardware or (as you already mentioned) BIOS. Perhaps a look in /proc/cpuinfo of both knoppix32 and 64 would help...? In the line "flags" it says something about supported commands for the cpu.
Perhaps there is a command set for 64bit support which is missing in your cpu? You could google for the sets your processor has to support.
Well, as I said, I don't think you'll find the problem this way but you could try anyway.