I think the steps you are using might be out of date? In the old days, the site icon was immediately to the left of the address in the address bar. But now there is a different icon there: a globe, or lock, or warning triangle. You now drag that icon to the desktop to create the shortcut. Does that work?

Try to hold down the Ctrl key while dragging to see if that works.

One other option is; On the desktop, create a new folder, you can call it something like Links. Open this folder and try to place the short-cut inside.

None of the suggestions worked, but when I reinstalled Internet Explorer 11 the shortcuts appeared. Now, however I can't drag and drop from Firefox.

You can look at this extension

• Deskcut: https://addons.mozilla.org/firefox/addon/deskcut/