Complete and unexpected System shutdown

Try pulling all but one memory module and see if there is any effect. If there is a bad module, try and isolate it and remove it. Just a hunch. :)

Navigate to c:/windows/minidump and see if there are any .dmp files .. if so zip them up and attach them to your next post for analysis...

just upload them anyway. Who know if solving issue with those BSODs will fix your instant shut down that you are suffering at this moment

Ok,
The DMP is way back in march therefore it's hard to conclude it's the problem you are having at this moment.
One of the DMP blamed the graphic card driver with stop code 116. One generic thing to try is to reinstall the driver, download the newest version of driver and install it on your system.
When upgrading your graphic driver you MUST remove all traces of the current driver. In order to do that we recommend using Guru3D - Driver Sweeper

When it is removed then download and install the fresh copy.

Another thing was blamed in the DMP was RapportPG64.sys. I've just done some research about this (coz it's hard to find), and I found out that it's some kind of malware, virus etc...and there is even an article talking about it and say it cause BSODs
MPECS Inc. Blog: Windows 7 BSODs – RapportPG64.sys is the Culprit
if you still have it on your system, I recommend to remove it.

What antivirus software you are currently using?

Since the symptom seem to be hardware, you should perform some hardware stress test:
H/W Diagnostics:
Please start by running these bootable hardware diagnostics:
Memory Diagnostics (read the details at the link)
HD Diagnostic (read the details at the link)

Also, please run one of these free, independent online malware scans to ensure that your current protection hasn't been compromised: Malware (read the details at the link)

BUGCHECK SUMMARY:

Code:

BugCheck 50, {fffff8a0157c0000, 0, fffff88001803dea, 0}

Unable to load image \??\C:\Program Files (x86)\Trusteer\Rapport\bin\RapportPG64.sys, Win32 error 0n2 
*** WARNING: Unable to verify timestamp for RapportPG64.sys
*** ERROR: Module load completed but symbols could not be loaded for RapportPG64.sys

Could not read faulting driver name 
Probably caused by : RapportPG64.sys ( RapportPG64+3dea )

Followup: MachineOwner 
---------
BugCheck 116, {fffffa8003af9380, fffff8800491b6c0, 0, d}

Unable to load image \SystemRoot\system32\DRIVERS\nvlddmkm.sys, Win32 error 0n2 
*** WARNING: Unable to verify timestamp for nvlddmkm.sys
*** ERROR: Module load completed but symbols could not be loaded for nvlddmkm.sys
Probably caused by : nvlddmkm.sys ( nvlddmkm+d06c0 )

Followup: MachineOwner 
---------

Regard,

Tuan

Just uninstall the display driver and install the new downloaded one.
Also, third party antivirus software are notorious cause for BSODs. I don't know how AVG has been working on your computer but it's just not an exception for that. Stop code 50 is potentially caused by antivirus. I would recommend to uninstall it for now and try Microsoft Security Essential, which is known for BSODs free. Please use it instead because we can eliminate a big potential cause.

AVG is known to cause BSOD, on some systems. I suggest that you uninstall it while trouble shooting using the uninstall tool > Info > Tool (32bit) - Tool (64 bit). If you have AVG Identity Protection installed, uninstall it also >Info > Tool. I recommend that you install MSE and make sure Windows Firewall is turned on.

Please let us know any news. Make sure to run the hardware diagnostic as I listed. For the memory diagnostic test, here is a short version of it in case you don't want to read the whole thing in the link I gave you earlier:
Download a copy of Memtest86 and burn the ISO to a CD using Iso Recorder or another ISO burning program. Boot from the CD, and leave it running for at least 5 or 6 passes.

Let us know if you need help

Tuan