After the computer boots up Windows (when it actually goes into log-in screen) a high pitched screeching sound appears. It's been very hard to locate the source of the sound within the case but I think it might be in between the first PCI-E port (where the GPU is obviously) and the processor. This sound has an "uptime" off maybe 80%, which makes it highly annoying. It can't be heard while in BIOS or safe-mode which makes me think this has something to do with the PCI-E port (or perhaps something else that handles the PCI-E input) and I'll tell you why.
The first thing I installed on the computer (game-wise) was WoW. As I first launched it I noticed a flickering on the screen. There were very subtle lines of white flashing horizontally as soon as the GPU-accelerated picture started up (in other words; log-in screen and in-game). This made me instantly think that it was the GPU who was the culprit. With the facts in hand I took out the GTX 560 Ti and went with the integrated graphics and voilá; no screeching sound (but I couldn't test WoW with integrated graphics).
For a moment I thought I had located the problem, but to make sure I wasn't wrong I installed a Radeon HD 5870. The noise was back again, as well as the flickering. I hooked up the computer with another monitor too, which in turn didn't give me anything, still the same problem.
I've also changed power-connectors to the GPU in case there might have been something wrong with them. Nothing.
So I am back to square one basically. My only reasonable explanation is that the mobo might be broken. Please, help a new PC builder to regain his confidence.
List of things I've done to exclude possible scenarios:
Tested another GPU
Switched out RAM
New connectors to GPU
Cleaning PCI-E and mobo with air pressure
Re-installed display drivers (both for AMD and Nvidia depending on what I had inside at the time)