Edit: Thread revived due to issue rearing its ugly head again.

Not a GOG game, though.

Here's the deal: Within 60 or so hours of playing Dark Souls, the game has crashed my entire system about 7-8 times. Every time my screen went nuts with colorful vertical stripes (mostly green) or just plain black, then white. Occasionally these crashes were accompanied by a deafening noise, consisting - as far as I can tell - of the last split-second of sound that has been playing right before the crash looping. Then Windows goes into freakout mode and just reboots.
I've only had this exact thing happen once before; it was caused by a glitch in Skyrim where some insane particle effect got stuck in a door or something. That was the only time it happened in that game, however, and since then only in Dark Souls where I don't have any other major performance issues.

Hardware.
AMD Radeon HD 7770 1GB
AMD FX-6300 @3.5 GHz
2x 4GB DDR3 RAM
500GB WD5000AAKS-60WWPA0 HDD
400 Watt be quiet! Power Non-Modular 80+ Bronze

My Windows (7 64bit) Event Log says it's Event ID 20 - WHEA-Logger. Fatal Hardware Error (a pleasant expression), AMD Northbridge.
WhoCrashed says:
This was probably caused by the following module: ntoskrnl.exe (nt+0x4B2B6C)
Bugcheck code: 0x124 (0x0, 0xFFFFFA8007DE7688, 0x0, 0x0)
Error: WHEA_UNCORRECTABLE_ERROR

Here's a list of random things I've done!
- changed resolution and other settings in the game
- ran memtest86 over night > no errors
- ran game with & without (in turn) GameBooster, RadeonPro, CCC
- scanned system with MBAM and Avast, nothing
- let Prime95 and FurMark run for about an hour and it was fine (though from what I hear, these should run longer?)
- all drivers are up to date (chipset & graphics recently updated)
- HDTune shows everything in green
- HWMonitor says temperatures are fine (GPU/CPU ~50°C, everything else way below that)
- sfc /scannow found nothing wrong

Nothing is overclocked. The GPU is maybe 3-4 years old now, CPU & PSU about two, the HDD & MoBo are probably the oldest parts in there. I regularly dust off the inside of the case. I'm not experiencing any other issues. Windows has been re-installed somewhat recently (half a year ago, maybe? That probably doesn't count as recently anymore).
I can run more demanding games (Far Cry 3, Tomb Raider 2013, Skyrim, New Vegas with all the texture mods) without trouble.

It seems so unlikely that a game would cause an issue that Windows deems "fatal", so mainly, I'm worried that there really is an underlying serious issue which will sooner or later cause more problems.

tl;dr: What exactly is Windows Event ID 20 and how do I fix it?

does hwmonitor show plot or only actual values?

You should check the minidump, which is unfortunately a bit of a PITA.
Also you could try running video memory stress test, although I don't know if that also checks the low level cache and such.
At first glance it looks like it's a problem with the GPU though.

Sounds a bit like what happens when my laptop overheats while gaming, though I just get a regular old blue screen. I think I get the event id 20 thing though. As far as I remember when it says fatal that just means it had to reboot / shutdown and not that your computer is dead.
Doesn't sound like it will be overheating, so as it's a hardware error it may be something failing or damaged. But that's about as far as I could say as my computer hardware knowledge is pretty poor...

Event ID 20 = worst game ever ported to pc, system shutting down in dismay.

Also sounds similar a little bit to what happened when it turned out a power cable to my graphics card was loose (colour stripes, then all goes black with a possible Windows reboot).

Check for that. Or maybe your power supply is failing?

ZFR might be right, try OCCT tests.
Also 400W might be not enough in your case, see Asus Recommended Power Supply Wattage Calculator says..

Thanks for all the replies. I don't know what that means! I'm quite the computer idiot, I can merely follow instructions. Is that not what WhoCrashed does without all the pain? Of course, it's a bit vague about it. Test stage 35 of 254 right now. That's slightly less worrying, then. No, I'm not getting that impression. Of course, at the exact moment of the crash, I have no way of telling, but unless the temps jump from "acceptable" to "meltdown" within seconds, it seems unlikely. I don't think Windows is that opinionated (yet) and if it were, it might not share your opinion. Huh. Will do. I would hope it's not the PSU itself, as it isn't that old and supposedly a good brand. Will do that too, after the VM Stress Test. Any suggestions on how long that should run?
That calculator now says min. 550W. Oddly enough, similar test range from 300-500W. The 400W PSU was recommended to me when I upgraded my CPU, I don't have the knowledge to make such decisions.

What seems odd is that if it is a hardware issue, why is nothing else going wrong - but I have limited knowledge. Very, very limited.

Not altogether; for example, when I was getting bluescreens with driver_power_state_failure every so often, WhoCrashed only managed to tell me the kernel was involved somewhere, and it took examination of the minidumps to work out that a dodgy Bluetooth driver was responsible.

Of course, that would make things too easy for me. How would I go about analyzing these files? The test has not returned any errors, came back with two "NOT SUPPORTED", though. Running OCCT atm.

Ah. I had CPU: OCCT on for an hour, then Power Supply for 15 minutes. It would have stopped, had it found an error, correct?
Guess I should do CPU: Linpack and GPU: 3D as well, for good measure?

For good measure tests should run at least for one hour, but since you survived power supply test you should be fine ; ) Do GPU test to be sure, with error check and fulscreen on.

Thank you for the continued assistance.
The, uh. GPU test seemed odd. Is the red ring supposed to be moving during that? Because it didn't; I got a still image and a blue ring cursor. Meanwhile, however, temperature, voltages and fan speeds went up like normal, the timer ran and FPS were displayed. o.0

That's ok, it doesn't move with error check on : ) If you didn't get any errors your HW should be fine.
Ignore the game or try playing it with different drivers ; )