I'm not sure if this item is maybe missing from the menu but could you check: right-click the desktop icon and look for Pin to Taskbar.

Note: that would not exist if it is a web page shortcut, only if it's the program icon.

I did right-click the desktop icon. the resulting drop-down menu did not show "pin to taskbar". I do not know if the desktop icon is a "web page" shortcut". I thought it appeared when I signed on to Firefox.

If you right-click the Firefox icon on the desktop and open Properties. Does Windows show the "Shortcut" tab and highlight the "Target"? In that case, it should work.

On the other hand, if you right-click the icon, choose Properties, and it opens a tab named Web Document and highlights the URL, that's a shortcut to a web page. You can't pin one of those.

If the desktop shortcut doesn't work, you can try this:

Open the Windows Start menu to All Programs and look for Mozilla Firefox in alphabetical order starting from the top of the list. Right-click that entry and look for Pin to Taskbar.

After right-clicking the desktop Firefox icon, as you suggested, I opened Properies and it did show Shortcut and highlighted Target. BUT, I still couldn't drag the icon to the taskbar. I tried your other suggestion and got a dropdown menu by rightclicking the Firefox listing on the start menu. But the menu listed "Unpin from Taskbar" !!!!

If that right-click context menu has Unpin from Taskbar, Windows thinks Firefox already is pinned to the Taskbar. Do you have a lot of pinned icons? I wonder whether it is getting shoved aside by something else.