sure you can give up, or you can look at the traces and follow the current from the place where it enters on the red wire. this is how everyone learned electronics.
it goes to the middle leg of that transistor. you could read the part number, google up the specs and use that to guess what it is doing. let us know.
then the adjacent three legged device in that heatsink appears to be a dual cathode schottky diode, and the current comes off that wide ground plane. what is the part number on that 8 pin IC, google up the specs and see if you can guess what is doing there.
the single big blue cap is the one that i figured was reversed, but we don't really know if you reversed the voltage polarity or put the 72V on the 12V output.
if that cap was reversed, it would be dead now. that was why i said you could test it to see if that is the problem. like i said, you can test a cap by using the ohmmeter scale on you meter.
ps: you only have to unsolder one leg, you can leave the other leg in the circuit and measure it that way.
use the high resistance range for the setting, unsolder the cap, put the red probe on the plus side of the cap, and if it shows a reading that is slowly increasing, you can reverse the probes and put the black probe tip on the plus of the cap briefly and see if the reading decreases as you do that.
if the cap is shorted it will show zero ohms resistance when you put the probes on it. if the cap is blown open circuit then the ohmmeter will not display a number, it will be over ranging.