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How can you tell its a switch mode PSU
In a "linear" power supply, making low-voltage DC, the AC wall-power input goes through switch and fuse to a big power transformer. The other side of that is low-volt AC. This goes to a rectifier, then to a big capacitor, and now you have low-volt DC. This may need to be further smoothed or regulated. But you can go through step-by-step and see what is happening, what isn't happening, and most of it is on the "safer" side of the transformer.
In a switcher, the AC wall-power input (almost always) goes to a filter-choke, because we don't want what is about to happen to leak back to the wall wires. You have a power switch here (many switchers don't). Then your 120VAC or 230VAC is directly rectified to 320VDC on the main capacitor. You could check this, but it is dangerous like sticking your finger in an outlet (even worse), and this part rarely fails. This 320VDC is "buzzed" at ~20KHz by a chip and a transistor or two, to excite a relatively small (compared to "linear" of similar power) transformer. The transformer isolates the wall-power from the chassis (this board has a White Line showing the division between un-safe wall-power parts and safer circuit-side parts, running under the transformer). The other side of the transformer has low-volt 20KHz AC. The bits on the left are rectifiers and caps to turn this into smooth low-volt DC. As an added frill, there is probably a feedback part from the low-volt side to the "buzz" transistor, to control its "ON" time and regulate the voltage at the low-volt side despite variations of load or line-voltage.
It is barely possible the actual path zig-zags from wall-power through switch to the transformer, and back to the rectifier and cap, then back to the left again. This seems unlikely, also the transformer looks too small (tranny size is related to frequency, and 20KHz AC takes a lot less core than 50Hz AC to carry the same power), also that choke right AT the power inlet is characteristic of nasty switchers that would wipe-out every AM radio in the house if their buzz got out to the power cord. (So are the box-caps below it, which seem to have been omitted here; perhaps their function is included in the large power-inlet connector.)
There are people here who actually design switching power controllers. I'm not one of them. I know the basic idea, but I don't understand the details nearly enough to diagnose one. And what seems to happen is a cascade of failures, whereas "linear" supplies usually fail at one point. If you have AC, but no DC, replace the rectifier. If it fails, you have a short; start cutting parts out until you get DC again, and then replace whatever was shorted. If you have DC but it is not smooth, replace the cap. But switcher theory is all dI/dV and hysteresis curves and special-spec transistors working at 101% of their ability..... as MCS says, a repair kit (if there is one) is usually all the power parts. Probably most of them failed, and it is easier to replace them all than to figure out which ones are truly bad.