AT LAST! Problem solved. At some point, a file somewhere had got corrupted and Knoppix was trying to use Rosegarden as its file manager for anything clicked from the desktop.

Control Panel - KDE Components - File Associations - inode - directory and remove Rosegarden, add Konqueror, and all is well. Phew!

It took a while to find, because "inode" is not a term I know.