Update. Holidays and such had me delayed in dealing with this problem.
I did return it to the store, and they couldn't recreate the problem, so no progress there. Only that the hardware seems to work fine.
I did mention the video card's fan sounding weird, and they replaced it with a new one which sounds allright now.
I've been trying other things, like replacing power cables, but that didn't help either.
Actually, the computer shut down once when working with a Window application, or even playing a DOS game (though with VDMS emulation) but it worked fine for several hours playing another game, that did demand alot of resources.
Such inconsistency in shutdowns sounds to me like some conflict on a certain software level. As final measure I intend to completly reinstall everything, but before doing that I would like trying reinstalling drivers and codecs.
How can I check if I removed all video and audio drivers and codecs? Over the years I've installed quite a few, and though I installed them all to the same spot, I can't see whether I truly removed a codec/driver or just a part of it.