Drag and Drop Test
OK, this is what I figured out. In the gnome Linux Mint 9, drag and drop does NOT work from the Desktop or if the file manager and firefox windows do not overlap.
But it does work if the file manager and the firefox winows DO overlap.

None of this works on a heavily-patched PCLinuxOS 2007 box with KDE 3.5.9 and Firefox 3.6.9. Because the PCLinuxOS is rather old and very far away from a vanilla install, I reckoned I should try something more modern like Linux Mint.
@leetee suggested that the problem might be that the drag and drop won't be supported from the Desktop so I tried drag and drop from the File Manager on both boxes. Linux Mint worked if the windows overlapped. But, alas, the ancient PCLinuxOS box was just too old and cranky and refused to work. Thank you for all your efforts, @paul. I think the mystery is solved. There is no more reason for you to do anything about this. It's a combination of user error and old software.
But it does work if the file manager and the firefox winows DO overlap.

None of this works on a heavily-patched PCLinuxOS 2007 box with KDE 3.5.9 and Firefox 3.6.9. Because the PCLinuxOS is rather old and very far away from a vanilla install, I reckoned I should try something more modern like Linux Mint.
@leetee suggested that the problem might be that the drag and drop won't be supported from the Desktop so I tried drag and drop from the File Manager on both boxes. Linux Mint worked if the windows overlapped. But, alas, the ancient PCLinuxOS box was just too old and cranky and refused to work. Thank you for all your efforts, @paul. I think the mystery is solved. There is no more reason for you to do anything about this. It's a combination of user error and old software.