Aaaah, I see what you're saying. I had it pictured differently.
I'm all for people trying to learn electronics... I'm learning every day. Anyone can do it with the proper time and effort.
Unfortunately, the switch mode power supply is one of the more complex architectures in the power world. It may be trickier to learn from it than with, say, a linear supply.
Not sure if this is a flyback or push-pull SMPS. Normally you'd see flyback in <150W supplies... but anything's possible. I can't tell if the TO-220's in the back are the switching FETs or maybe even secondary side rectifiers.
I can't say for sure what the FET in question is doing, based on his location on the PCB. If you can get a good picture of the traces on the back (the entire PCB,) and a top-down view of the whole primary side (with all the components on it) maybe I can make a guess, and we can figure out your mystery resistor.
Who knows, someone else on this board may be able to say "Oh, that FET is the ______, and it's doing ______." But it's not standing out to me. Don't give up hope. hehe.
The black char mark on the PCB doesn't look promising either. Usually not a good sign when things are producing that kind of heat. Don't know if that was a one-off when the supply blew up, or if it's an "over time" deal. What looks like a diode, just below the resistor, has also started to char the PCB.
I would definitely expect some cascading failures with this one. But it may be as simple as a shorted switching FET and a diode or two.