I doubt that the image files on the mirrors are corrupt -- simply on the evidence that there would be massive discussion of that problem on this forum if that were the case.

You used different hardware to burn the CDs. Have you also tried booting the CDs on different computers? (You probably have . . . but if you haven't, I'd try that first!)

You say the checksums match. How are you testing that? If you haven't already, try running the Knoppix CD with the cheatcode "testcd" (that is, at the Knoppix boot prompt, type "knoppix testcd"). I'm not certain, but I think this will perform a bit more than a checksum test. Keep your eyes on the screen, though. The test takes a couple of minutes, and after it displays its verdict the booting continues, which scrolls the information off the screen.