Repairing a failed generic AC/DC power supply which "ticks"
I'd suggest that the ticking is the power supply trying to start up, but hitting an instantaneous overcurrent limit. A good power converter will protect itself from running into a dead short, which could overheat components very quickly. Many transistor drivers have built-in desaturation protection, turning off the transistor for a set period in case the voltage across the transistor gets higher than it should be during on-state.

To do a full analysis, you'd need to develop a schematic of the circuit. Once you know what topology you're working with, and what's driving what where, you can start to debug. I'd get a scope and look at the output of the circuit while it's ticking, to observe whether any voltage at all is developing there. If the supply has multiple output rails, check them all. Then work backward through the circuit until you find the transistors and their drive circuitry. See whether the transistors are all being gated on, and if they stay in saturation during that time.