Power supplies are fairly simple devices. There could be many things causing this, but I will try explaining to you how to try and find the fault without using fancy tools. Firstly do another inspection and look for any tiny burn spots or cracked solder joints. If you find those, either the solder joint or the component that is on that joint is defective. If that is all fine, buy some alchohol(idealy 99% isopropyl, but ethanol should work as well). Apply it to the components on the board, turn the power on and try turning the power supply on(in case it has a switch). Once you do that look at the alchohol. Where it evaporates first is probably the fault. In case you can't find out anything like that, fault is more complex and definetly requires a good multimeter and perhaps an osciloscope to diagnose. But I believe you will find the fault with alchohol method. Good luck.