I would agree with the STF4N90K5 in TO-220FP package.
I suggest you remove the mosfet and measure again to confirm no other shorts.
From any DC capacitor after the rectifier, you measure ohms to make sure that the capacitor charges up to high enough ohms and not shorted or low ohms. If there are still shorts, the DC capacitors will show a short, meaning cannot turn power on. But still cursory measure each mosfet to be double sure, no more shorts.
Have you already study the auxiliary power supply at least it can output the voltage at the DC capacitor after the regulator or rectifier of the auxiliary supply?
You can isolate the main switching side by taking out some fuse or connector. Just test the auxiliary power supply for function.
Now you have the isolation transformer ready, you can use it to test it.
Be safe and take your time.
I always will forget to unplug and discharge capacitor after test. I think I need to tie a red string on my thumb for reminder.
Wear a rubber glove and a safety goggle to add confident level.