Well, I actually don't see any blue screen (the screen becomes rather white, than blue), the game just hangs my system up, so even the reset button doesn't help and I have to turn the power off and then in.

To me it happens at the starting zone of the module Legacy of White Plume Mountain. I do nothing just level up my party and buy the stuff. It's happened 4 times already in less than an hour.

In the comments for that module's download page, users reported strange crashes, but several of them said that reducing the graphics settings prevented the crashes for some reason. It does seem to be a tricky one to get running. You might have a better time with Misery Stone.

Yeah, but as far as I understand, Misery Stone is pretty short.

So I got the same problem with all other campaigns and modules. I think, it's not even BSoD, the game just freezes my comp, the screen becomes white, and I hear just a hum instead of sounds.

A couple of times it was even more weird. My comp didn't freeze, but my monitor got shut down as though I turned the PC off, but I still could hear the game.

I think, this things mostly happen on locations with low and heavy environmental sounds, like dungeons or mountains (that wind sound), but I'm not sure, that's the reason of my problems, but I never experienced problems on Neverwinter (the city) locations. And as soon as I went to the wild, I got 5 or 6 freezes.

One time it almost happened, when I used a healer's kit, but the game got back to working in a few seconds.

I've heard of, and even experienced personally once (with a different game), games locking up computers due to sound effects. For me the solution was updating my system sound drivers, but in cases where your sound drivers are already on the latest version, it may work to roll back to an earlier version.