How to check the bridge rectifier: put your multimeter in 'diode' mode. This will test the forward voltage. You test between the '~' and '+'. You should see a value (e.g. 300 to 700, depending on whether this is schottky or silicon rectifier) when red probe is on '+' and black probe is on '~'. When you reverse the probes, you should not see a value respectively OL (over limit).
Then check between '~' and '-'. This time, you should see a value with black on '-' and red on '~', and OL when reversed. If you see a low value in both directions, the internal diode is blown.
You can apply this rule to each diode.
You can check the capacitors in Ohm setting. When first connecting the probes, the value might be low, but then rise continually as the capacitor is charging. Note that if you test capacitors in-circuit (i.e. you didn't desolder), you may have other components impacting on them, so in-circuit measurement isn't very reliable if you don't know the circuit. But it's a good start. Only if the values show very low ohmic (in the ohms or some 10 ohms range), i would desolder and check.
Your AC portion is nearly identical with mine, see schematic. You can identify the large 450V capacitors C6 and C7, indicated with + and -.
You can also find the two MOSFETS T1 and T3, and I indicated G,S,D.
The MOSFET (power transistor) has 3 pins.One is "Gate" (G), which is the control input. Normally, the circuit board track to this pin will be narrow/thin. The other 2 pins are "Drain" (D) and "Source" (S). The PCB tracks to these pins will be wide/thick. However, on your board, the thick tracks are all concealed by the heatsink, so it is difficult to tell which pin is what. But you can still check the mosfets relatively easily, when you consider how they are connected.
T1 will switch the "+" 300V to the common pin of the transformer winding, and T3 will switch the nagative line (actually 0V, GND). You can see that S of T1 and D of T3 are together on this winding. So in your circuit, check which S and D are together, and you know which one is T1 and which one T3. To confirm, check that D of T1 goes to + of the capacitors, and S of T3 goes to - of the capacitors.
If you measure diode between D and S, it likely behaves like a diode, see behavior above. Check Ohms, too. If you see ~0 Ohms in both directions, this is spoilt.
Between G and S, you will see the 10kOhm resistor (marking: 103), or even lower ohms. Between G and D, it should be high ohmic (Megaohm).
If you have done those components, I would hope that you have found the culprit.
Sometimes also the diode on the secondary side short circuits. These are often 3-pin components (double diodes) with large heatsink. In the schematic, it is D3 & D5. check each of them.
Yours are two double-diodes, standing, with the heatsink, next to the 3 brown and 2 silver/blue capacitors. Check each of them. The middle pin (2) is common. So pin 1 and 3 should have a diode behavior towards pin 2.
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