Switching power supply repair
Common problems with these power supplies I've encountered are:

high value (100k+) resistors going open circuit. There is normally 2 resistors in series to give adequate voltage rating, but some have only one resistor. These rsistors can be difficult to measure in circuit - unsolder one end and measure.

The resistors in question are the 'kick start' - they give enough voltage to the switcher ic to start up. Once started, a winding on the main transformer is used along with a diode and capacitor to supply the switching ic from then on. The capacitor (usually 47-100uF 25-50V) can dry out. The power supply normally hiccups in this case.

Output diodes gone short circuit. This will shut the supply down quick sticks. Measure the diodes. Usually these are TO220 pkg dual diodes for the main high current output.

Main input capacitors drying out. If this happens with a psu topology like yours, then the switching transistors vapourise. You can replace the transistors but they keep on blowing until you replace the electrolytic caps.


Note that some power supplies don't like starting into no load. Some big resistors or some automotive light bulbs can suffice for a dummy load.
Sometimes you get a random failure. In this instance it a matter of testing each component. You can test the switcher ic by powering from a bench supply - read the chip's datasheet to see what voltage it requires - usually 12-15V. Use an oscilloscope to see if the ic is outputting pwm to the transistors. Make sure the power supply itself is NOT powered by mains voltage!