This error in my experience is user error although CPanel doesn't help, this message doesn't give you much to go on.
Let's talk more about the process of setting up SSL with CPanel.
It sounds simple if you know how to do it but what happens if say you delete your private key after generating the CSR?
With some clients this does happen and they end up using their CSR as their Private Key .key file which doesn't work of course. It also doesn't help that once you delete a CSR the corresponding private key is deleted with it and CPanel doesn't warn the user.
In either case if things aren't working the chances are that you/the client has mixed up the different certificates. The best thing to do is to start over with a new Private Key (make sure you save it) and new CSR.