Nothing you have done with the adapter or mains cables has caused the damage/fault so just return it for a replacement - or get a different monitor if there are other reports of failure. There's no point in mentioning the adapter or the Euro mains cable to the supplier as it's not relevant.
surly if it isn't showing its self test when you turn it on its broken, if you press any of the adjustment buttons does it show them?
You have a backlight, so you know that the monitor has power. You can rule out any problem with the power cord. The power cord is fine.
You know that your PC HDMI (video) output works, because you have plugged another monitor in and that works.
If you haven't already done so, you need to check that the HDMI lead is good. Set both monitors up near the PC, get the good one working, and the bad one with backlight but no image (and no HDMI lead plugged in. Now transfer the HDMI lead from the good monitor to the bad one. If you still get no picture, the monitor is faulty & it won't be anything you did to it.
Send it back for replacement or refund.
P.S. You have RTFM & tried cycling through the input sources haven't you?
I've already tried multiple cables, both HDMI and DirectPort.
I don't know what RTFM is, but I've tried bringing up the menu from the buttons and there is nothing showing up, so no image at all.
I've already ordered another monitor from another brand (it seems like Gigabyte are notoriously bad at customer support - something that came up while I was trying to figure out what was wrong with the aforementioned motherboard, which is also from Gigabyte, although they responded to me very quickly when asked about the motherboard, but not the monitor - different departments, perhaps?) and I'll be returning this one to amazon. Hopefully this one will be fine. As an aside, I've been researching monitors lately as I do want to get something half decent and there seem to be issues with most of them. I don't necessarily know if that was the case a few years ago when I last bought one.