Machine_Check_Exception BSOD, and random shutdowns during gaming

I recently built a new computer with the following specs:

Intel core i7-930
ATI Radeon HD 5870
Asus Rampage III Gene mATX motherboard
Kingston HyperX 6GB (3x2GB) DDR3 1600 memory
Corsair 650W power supply
Intel X25-M 80 GB solid state drive
Windows 7 Home Premium 64-bit

I've been having issues with it during (and ONLY during) playing computer games. It will often randomly initiate a soft Windows shutdown in the middle of any game, or blue screen with a "Machine_Check_Exception" error message. These will always be preceded by a 'droning' sound from the speakers that lasts for a split second, which will occur sporadically for a minute or two until either the computer shuts down, or freezes and blue screens. When I am not playing a game, the computer has zero issues. However, when streaming video from Netflix or Youtube, I will very occasionally hear that same 'droning' noise, but no error will occur.

This problem has occurred with multiple video cards, and still happened after I got a replacement processor from Newegg, so I've ruled out the issue being my video card or CPU. I also think it is unlikely that it is a temperature problem, because I've been running a temperature monitor and the issue will occur regardless of what the temperature is, and the temperatures themselves are not high enough to be of concern. I've been dealing with this problem for over a month now. Any advice would be greatly appreciated.

I've attached minidumps from the several times the computer blue screened. Usually though, it will just rapidly shutdown by itself as if I pressed "shut down" on the start menu and give no error message upon restart. Thanks again for your time.

edit: I also thought I should mention that I am generally able to play games without problem for extended periods immediately after restarting the computer. However, after the computer has been on for some time, the problems begin.
 

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Please place your minidumps in one zip file. Also, have you overclocked any of your components? What are your temperatures like?
 
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