Don't RAM problems usually end in blue screens? Not shutdowns? To me this would lean my "weird shit-o-meter" towards mobo socket bad. Someone earlier was talking that it might be your memory controller, granted I am way behind on modern CPU design, but I thought intell's memory controllers were still on the northbridge not on the die itself. If not this could be an issue too.
The only thing you can do to eliminate RAM as the problem is to not put your ram in the "suspect" Ram slot, and rotate all of your ram sticks through every other slot and do your test that crashes it. If all combinations don't work, I'd say your RAM is okay. There's also a program you can boot from disk or floppy (http://www.memtest.org/) that checks every single memory address. You can try running this program while only having 1 stick of RAM in at a time in a known good slot to test the sticks themselves. Then put 1 stick in the "Bad" slot and try again. Some mobos you have to have a stick in like "slot 1" at least but then can have 1 in any other slot, if this is the case well just use 2 sticks.
You've got to eliminate all possibilities since there are multiple things that could be failures.
Idk... I think it's an outside shot, but I really think there may be an underlying power issue somewhere. Usually RAM issues cause blue screens, not power shorting issues.
Actually here's something... have you tried re-seating your motherboard? It will probably require you to re-set your heat sink which will mean re-applying the thermal paste, but if your Mobo isn't mounted properly something could be shorting the motherboard to the case, if it's the right solder point I guess it feasibly could be related to a ram slot you're accessing.
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