My main suspicion therefore is the memory, since it is not a 4x4GB kit, but rather 4 sticks of the same memory modules (essentially 4 'kits' of 1 stick each).
The CPU works completely fine and functions as expected when stresstested (Cinebench R20 on loop), same goes for the GPU (Unigine Heaven on loop). Populating all 4 slots causes the system to stutter, freeze, video output to cut in and out intermittently, and usually ends in the PC just restarting itself (I'm assuming it BSODs, however I cant verify this, since it happens when the video cuts out, and the next time I get video out, it shows the system at the motherboard splash screen). I recently assembled a PC at work, and it's been incredibly unhappy when I fill all 4 DIMM slots with memory modules.