I wouldn't worry about it; IDK how it would know there's a reversal, really.
The italian plug goes in either way, so technically, it should show the opposite if you flip it over.
Regardless, there is no reason to worry about that polarity; It matters in the USA system, but not that one, due to the way our power is designed.
The monitor I repaired last night will work equally well with phase connected to either input wire, and it will work on 110-250V, with no changes.
The ground is connected to the chassis, as a safety; if a wire comes loose internally and touches the case, it's supposed to blow a fuse or turn off the outlet if it's GFI.
Almost everything globally is designed this way now; the internal switching power supply provides isolation from the AC power.
Short version (too late!): The input power is not related to your power supply problems.
Longer discussion on household power, for the curious.
All household power comes from an outdoor transformer, that drops power from a high voltage (7500V 60Hz here) to household voltage.
USA Household voltage is based on the old 1800s carbon filament light bulb voltage. It was 100VAC, 25Hz.
Transformers for 25Hz are huge, so we went to 60Hz early this century; the last 25Hz generators were at Niagara Falls, IDK if they're still there or not.
No, it's gone:
http://www.technology.niagarac.on.ca/people/mcsele/interest/rankine-generating-station/
So, modern 115VAC 60Hz is based on that. We have the Secondary transformer center-tapped, with the center tap connected to Earth Ground at the Meter box.
This gives two opposite 115V phases, or a 230V phase across both.
If you touch either phase wire while standing on the ground, you get 115V, and it can kill you.
European power is similar, but it's 220V 50Hz, and the transformer secondary is not center-tapped or grounded.
The advantage is you don't get shocked if you only get one wire.
And wires can be smaller, for higher powered stuff.
There's more complicated power for industrial stuff, but it's not in most houses; they won't run me 480 three phase to my house, even though it's on the pole outside, lol.
Lathes, Drill presses, Bandsaws, etc. that need 3 phase power are cheap on ebay.
