If you have an output that is always ON, then the relay contacts have welded closed. The otehr outputs that won't come on, I suggest are relay contacts that are burnt out.
My suspicion is that this unit has been powering devices without proper suppression on its outputs.
Even if it is under warranty, I doubt it will be exchanged, the relay contacts appear to have been "abused" out of specification.
You can most definitely hear the relays clicking on these units. When I had one, I was going to replace the relays with solid-state ones, so took it apart to see how difficult a job it would be. Someone with de-soldering and soldering skills (TV repair shop?) should be able to replace the relays no trouble.