Sometimes you come across something weird and this was definitely one of those instances.  I honestly don't know what I did to get here but I found myself unable to drag and drop icons.  I attempted to drag an item to the recycle bin but no such luck.

After a couple of quick searches I discovered this fix:

1.  Find an item you're unable to drag.
2.  Click on the item with your left mouse button and hold the button down.
3.  Hit the ESC key while you're holding the mouse button.