Given my experience as an IT Technician, an old hat I don't wear any more (there's no money in building and fixing computers) I would say that a logic board is a logic board is a logic board. There is nothing on that board that is 110volt specific, so it should be a straight swap.
The difference between system software is that European iterations of the system software called the trash can a "waste basket" among the common annoyances of running system software from Europe, but in terms of functionality it should be much the same.
That type of thing generally happens when you have a crack in the circuit board. It's not completing the circuit and so its failing. It can also happen if the plug connection is faulty. The first option there's nothing you can do and generally you would replace the entire power supply unit, the later option you can resolder the plug back on properly and go from there.
I don't generally open up PSUs as they contain capacitors that hold many thousands of volts and high amperage that if you touch will result in death. Broken power supplies are easily replaced, check eBay and the usual places. Much easier to replace a power supply than to replace your life.