Thanks very much for that link, Xandrios,
trying to ingest the information on that russian forum
perhaps the replaceing of a 100uF capacitor mentioned there will do the trick. Dryed ElCap sounds very familiar.
Edit: Indeed, when a 100uF 25V capacitor is soldered to the board as shown in the picture in above link, the PS can be brought back to life
When mains is applied, a click is heard, the 3,3V and 5V standby voltages re-appear and the PS can be switched on the usual way.
Now I just have to find a way to replace the failing capacitor in a proper way - It is located in a very unreachable place in the center of the board.
Again, thanks for pointing out that link, Xandrios