Every once in a while when I'll try to drag and drop something like an email in my Outlook Inbox to a sub-folder, or drag and drop files in my GUI FTP program and it just won't work.
My fix was just to hit the Escape key on my keyboard a few time. Poof! I can now drag and drop again.
If this doesn't work for you, make sure that one of the special keys like Alt or Ctrl aren't stuck.
Drag and drop away.