This happened to me yesterday.
In Windows Explorer, click a file with the left mouse button and keep the button held down. Then press the Escape key. Drag and drop is miraculously re-enabled.
I think just pressing the escape will work too but I'm no longer in a position to test that. I got this from http://it.thelibrarie.com/weblog/2010/06/drag-and-drop-stops-working/