Quite unexpectedly a chap from a parcel service rang my bell and brought me a brand-new iiyama monitor while taking away the old and broken one. iiyama actually promised to call me when they'd have this monitor model on stock again. They never did but just replacing it is also quite ok with me.
$iiyama == 3 now. I am quite eager to see how many monitors I can make them replace within this three years of warranty.
PS: I observe the same thing Rafael did. The new monitor is by a magnitude brighter than the old one. It's now so shiny, I love it! But maybe it's just a thing with the factory settings that seem to be better than the custom settings I used. They have contrast set to the maximum and brightness to a rather moderate value. I remember that I used lower contrast and higher brightness for some reason.