BSOD Seemingly At Random, error KMODE_EXCEPTION_NOT_HANDLED

Did you update your Graphic Card driver ?

If safe mode works for prolonged periods then thats a good sign, i would recommend you remove the Gigabyte software especially easytune its installed a really old driver on your system (2006) thats not going to help matters, if BSODs are still occuring after that then driver verifier may give us some more clues, i think you may have slightly misunderstood its purpose, its job is to cause stress on drivers in the hope of causing a crash and then if/when it does it can often generate a more accurate dump file that can specify the faulting driver instead of just generalising and blaming the kernel upon which they crashed. It will make the system slow and sluggish but thats the idea and may give us some more info

Free up the startup. Windows does not need any other program to auto start with it, but the auto start programs often conflicts and causes various problems including BSODs.

1. Click on the Start button
2. Type “msconfig (without quotes), click the resulting link. It will open the System Configuration window.
3. Select the “Startup” tab.
4. Deselect all items other than the antivirus. All, but not MSC.
5. Apply > OK
6. Accept then restart.

A stop 0x3B is very common, and it is some of the cases very difficult to debug, at is is related to a display driver mostly (as in your case). So we can try to attempt for a most perfect driver installation only. According to Carrona.org,

Cause
This error has been linked to excessive paged pool usage and may occur due to user-mode graphics drivers crossing over and passing bad data to the kernel code.

Install the latest WHQL of the display driver only.

• Uninstall All nvidia items in Control Panel > Programs and features
  
  • 3D Vision Control Driver
  • 3D Vision Driver
  • Graphics Driver
  • HD Audio Driver
  • PhysX
  • nvidia Update
  
  (Are you using nvidia chipset drivers? If so, dont uninstall anything other than those are listed).
• Reboot. Now follow Drivers - Clean Left over Files after Uninstalling
• Boot normally now. Go to Drivers - Download NVIDIA Drivers, Download 314.22 WHQL. While installing, Select Custom (Advanced) install. In the next page, follow this settings:
  
  
• During uninstall and install, accept all the offered reboots.

Also, Stress test the Graphics Card using Furmark.
Video Card - Stress Test with Furmark

Check if the Power Supply Unit (PSU) supplying adequate power to the computer or not.
eXtreme Power Supply Calculator
At least 30% excess is safe.

Is the computer hot? Report us the heat of the computer after a couple of hours of your normal usage. Upload a screenshot of the summery tab of Speccy.

Intel RST AHCI driver is a failing module here.

Code:

fffff880`0374dd88  fffff880`0106325bUnable to load image \SystemRoot\system32\DRIVERS\iaStor.sys, Win32 error 0n2
*** WARNING: Unable to verify timestamp for iaStor.sys
*** ERROR: Module load completed but symbols could not be loaded for iaStor.sys
 iaStor+0x2e25b

Download and install this particular versionof Intel Rapid Storage Driver:

• Version: 11.2.0.1006
• Date: 06/11/2012

Also, seeing frequent storage related errors.

Code:

fffff880`0374ea08  fffff880`0151d6df fltmgr!FltpDispatch+0xcf
fffff880`0374e978  fffff880`0151ebcf fltmgr!FltpLegacyProcessingAfterPreCallbacksCompleted+0x24f

I think you should not use Marvell 91xx SATA 6G Controller. (SCSI Controller)


No code has to be inserted here.



So this driver should not be present there. Uninstall Marvell. Then follow Drivers - Clean Left over Files after Uninstalling

Let us know the situation when done.