Problem solved!! :thumbsup:
The unblock-thing did the trick!

Thank you very much helping me to solve this problem :D

I did not, because I don't know how to unblock files. I do not even know what it is...

No, that option is not available. What I tried was to examine other icons and check their sizes.
The steam-icon was 32x32 2 bits so I made a icon from that size, but it did not work. That means the...

Nope, did not work, but I am not sure if I did it right. I opened a new icon in icofc and the program came up with the choice of the format. I choosed 24x24.
After that I instantly saved it ,...

Yes, I am trying at this very moment to create an icon with an icon-editor ( IcoFx ) . I try 24x24 pixels
I did copy the previous icon into Windows\System32, so that should be okay.

Yes, I did. Same story as others: I got a small white square, so I wondered if the size of the icon got anything to do with it.

As I have the same problem with my 64 bits system, I wanted to try this 'empty.ico' but the link is now dead.
Please can you put a new link up? Thank you.