I can tell, this was a really strange experience.
I wasn't able to find a service manual, or a schematic for it, so I needed to jump into it blindly. Opened the box. It has a huge toroidal transformer in the center, a board with two big heatsinks, capacitors, power transistors, and rectifiers at the back, and two stacked boards screwed to the front panel - this is are the control boards.
As I have no schematic drawing, I tried to isolate the problem. My first idea was, to change the connectors on the two, electronically identical (I guess) sides. With this I can localize the problem - controller part or power part.
Every attempt I take to switch the sides was failing. When I switched the connectors, the controller was working, but the channels hasn't started. Then I found a single transistor (or a dual diode, I don't know) connected to the power board with a connector and not soldered in. When I disconnected, the relays of the dead channel started to work. Switched slowly, but worked. Reconnected the device, and the relays still worked. The channel, came back to live.
When I switched off and on, the output switch, it the originally dead channel was always working, but switching on, was much slower that the good ones. After switching it on and off several times, the channel became as fast as the other.
One thing became clear. In the near future I'll have to buy or build a lab power supply, because this is not a satisfactory situation.