The problem is a failed MOSFET on the secondary, which fails short. Thankfully the PSU has short circuit protection, that's why you hear the click. Check the output with a multimeter, you will likely see a shorted output. If so then the fault is most likely one of these MOSFETs.

This can be repaired pretty easily with a hot air rework station, some experience doing these sort of repairs, and some patience as the MOSFETs are pretty solidly soldered to the board and surrounded by large copper planes. An easy way to check to see which MOSFET failed is to probe between the gate and the drain or source (just use a nearby heatsink); the failed MOSFET will show ~4.4ohms lower, as the working units will pass through two 2.2ohm resistors in series, the failed one will be low impedence to the source and drain. I took a working MOSFET from one failed PSU and transplanted it into another, and now I have a working PSU and another PSU for spares.