Other than how tight it's packed, it probably should be a pretty standard layout SMPS with a chip or two, having most of the circuitry, inside them.
That little 8 pin chip on the top side, next to a small transformer, that should be the primary side controller, that gets some trickle of current from after the rectifier, as it's startup Vcc, then once it gets going, some winding on one of those transformers, will generate the working Vcc of the chip, and circuits around it.
Does it have a Standby voltage on the secondary side ? That little transformer by the 8pin DIP could be for STBY, or it could be some gate drive transformer, but it looks big for that.
That chip could just be for STBY 5V, and there's another chip doing the main switching of the big transformer.
You don't have to plug it in, to check a bunch of stuff like for shorts or diode voltages, from the plug, inwards, to those big transformers. And same with the output side, starting from the transformers.
Then if there's no apparent shorts,etc, I would solder on a few wires here and there, and power it up and check some voltages, like after the rectifier, and Vcc of any IC's.
So does the other one do anything at all ? And noise, or does it try to make some voltages and then restart over and over ? If it's totally dead, something near the plug should be broken, like a fuse, or the rectifier.