you wrote :
When I start Kaffeine, the icon bounces for half a minute, then the app quits without any error messages.
As a user under KDE session, the error messages are logged in in the file : /home/<user_name>/.xsession-errors
Post what concerns Kaffeine in this file when you try to run it.
Or run it in a Konsole under user login not root.
I ran it as root and got the error message
Failed to connect to X-Server
Do you run it in a root console ? Because that can't work with a graphical program.
Run as a different user
Then click the Run button
Or instead of all this, in a user Konsole :
Without the exact error messages we cannot go further at this time. So post again with the required infos.