I reinstalled it and will do some testing. So far I removed my external soundcard and it still failed the test, same with my mouse. My external hard drive also seems to have no impact. The situation with BSODs seemed to improve after the uninstall actually, but just now it has become worse and I'm seeing behavior that I haven't experienced before.
First, I get freezes (only solution was hitting reset) and crashes (BSOD) while gaming which so far wasn't common at all - it would crash only after a session. Second, today I got a Red Screen of Death - any significant difference between it and a standard BSOD? Third, after hitting reset, a few times my BIOS settings got cleared which I though was unusual. I'm running almost the latest version of BIOS by the way, and will update it to 1 version later one (it doesn't seem to have anything relevant in its changelog though). And fourth, I've experienced freezes while being in BIOS which required resetting.
Could this be a hardware problem? RAM? Motherboard? CPU? PSU?
I think I will run Memtest. I recall running it before without any specific errors, but maybe I didn't run it long enough.
EDIT
Also, I've been experiencing it for some time but didn't find it too annoying, but sometimes the boot procedure would halt upon displaying "Detecting USB controllers..." message (1st screen), sometimes at a flashing cursor right before the Windows boot animation screen, but sometimes - while displaying Starting Windows but the animation not appearing at all. If I recall correctly, most of the time it happens when booting cold, eg, after being switched off for a night. Reset makes it boot just fine though.
EDIT #2
Actually, now that I think about it again, it think the Memtest performed some time ago did give some errors after approx. 16h. It happened with 1 stick which I suspected to be faulty and I tried other RAM sticks from a different PC, which runs fine, and I still got BSODs. And the supposedly faulty stick didn't cause BSODs on two different PCs either. So after reformatting and reinstalling Windows everything ran very well and for some reason I dismissed thing finding...