Thanks for YOUR patience. I am in no hurry, but I admit that this is a challenge.
I am sure that the .ds file is significant. I had installed a different (incompatible) scanner driver and there was a different ds file in TWAIN_32 and a different handle for the scanner to be chosen in the application. As soon as I deleted the registry key, it was gone.
BTW, the registry of XP is very similar to the Win2K. But the F4580 did not install any TWAIN driver on the XP laptop, so there is nothing to replicate. The installation was done automatically and I did not even see an option for TWAIN.
As I am stuck, I cannot think of any additional information.