Guys,
Thank you for your help. I got the help from the Forum three times just to start using Knoppix. And all times I declared: Now it works. But never say it works. And now I got the next problem, just to make Knoppix live.

Yes, my SATA HDs had been detected. The clue was Knoppix 3.7 with cheatcodes knoppix26 and the weird acpi=off (Hello, Windows!!!)
It even had detected my USB flash drive. So, I reported success here.

Sheesh! When I connected my USB external drive and reloaded OS, the drive was not detected. I had no problem with the drive using Knoppix 3.4 (old kernel)

Please, please. My wishes are extremely modest. I just want to have my Linux box running. With SATA and external USB hard drives. Is it too much???