How do I remove the Never-Ending Dropbox Folder?

Are you doing a full delete or a recycling bin delete? If it's trying to shift the folders to the recycling bin that could be causing the problem with "the destination folder...". Try Shift+Del instead of just Del.

Next, I would try booting off of a Linux LiveCD which supports NTFS (Ubuntu should work), and try deleting the folders from there. Since Linux doesn't have the same filesystem restrictions as Windows, it may be able to delete the folders even though you can't in Windows.

If you are using one Dropbox profile on two or more computers at the same time, turn off all computers except one and delete the file.