The new KDE 4.x window manager has changed the way the Desktop is managed. A widget called folder-view shows the contents of the ~/Desktop folder on the physical desktop (i.e. on screen). However this prevents drag and dropping files in the ImageJ window. The problem is that the string pointing to the file is not the directory name itself, but handled as a kio slave called desktop: (note the colon).
The solution to this is to change the settings of the folder-view widget:
You now can drag and drop files from the Desktop shown on the screen.