BSOD while playing League of Legends and freezing with other program

This all started a couple days ago when I was running a pretty RAM intensive program and it would always freeze up on me after couple of minutes. I've updated my drivers couple of days ago but I'm not sure if it had anything to do with this. Now whenever I play League of Legends, couple of minutes into the game the screen freezes up and gives me BSOD. I checked my minidump files on WhoCrashed and it seems like this program called ntoskrnl.exe is always causing the crash. Here are the results I got on WhoCrashed:

On Mon 4/13/2015 6:02:12 AM GMT your computer crashed
crash dump file: C:\Windows\Minidump\041215-18018-01.dmp
This was probably caused by the following module: ntoskrnl.exe (nt+0x6F880)
Bugcheck code: 0x1A (0x41201, 0xFFFFF683FF7B1A08, 0xF7A0000200E30005, 0xFFFFFA8009D71980)
Error: MEMORY_MANAGEMENT
file path: C:\Windows\system32\ntoskrnl.exe
product: Microsoft® Windows® Operating System
company: Microsoft Corporation
description: NT Kernel & System
Bug check description: This indicates that a severe memory management error occurred.
This might be a case of memory corruption. More often memory corruption happens because of software errors in buggy drivers, not because of faulty RAM modules.
The crash took place in the Windows kernel. Possibly this problem is caused by another driver that cannot be identified at this time.



On Sun 4/12/2015 5:35:03 AM GMT your computer crashed
crash dump file: C:\Windows\Minidump\041115-28048-01.dmp
This was probably caused by the following module: ntoskrnl.exe (nt+0x6F880)
Bugcheck code: 0x1 (0x7730FC9A, 0x0, 0xFFFF, 0xFFFFF88009880CA0)
Error: APC_INDEX_MISMATCH
file path: C:\Windows\system32\ntoskrnl.exe
product: Microsoft® Windows® Operating System
company: Microsoft Corporation
description: NT Kernel & System
Bug check description: This indicates that there has been a mismatch in the APC state index.
The crash took place in the Windows kernel. Possibly this problem is caused by another driver that cannot be identified at this time.



On Sat 4/11/2015 8:12:28 AM GMT your computer crashed
crash dump file: C:\Windows\Minidump\041115-20420-01.dmp
This was probably caused by the following module: ntoskrnl.exe (nt+0x6F880)
Bugcheck code: 0xA (0xFFFFF8000027C608, 0x2, 0x1, 0xFFFFF800030DF20C)
Error: IRQL_NOT_LESS_OR_EQUAL
file path: C:\Windows\system32\ntoskrnl.exe
product: Microsoft® Windows® Operating System
company: Microsoft Corporation
description: NT Kernel & System
Bug check description: This indicates that Microsoft Windows or a kernel-mode driver accessed paged memory at DISPATCH_LEVEL or above.
This appears to be a typical software driver bug and is not likely to be caused by a hardware problem.
The crash took place in the Windows kernel. Possibly this problem is caused by another driver that cannot be identified at this time.

I ran 2 passes of memtest+ for each of my RAM sticks (I have four) on the first slot and then I ran all four of them for another 2 passes but I got no errors. My drivers are all updated and I got the latest BIOS from the manufacturer page.

Additional information is required.

1. Download the DM Log Collector application to your desktop by clicking the link below

DM Log Collector.exe

2. Run it by double-clicking the icon on your desktop, and follow the prompts.
3. Locate the .ZIP file that is created on your desktop, and upload it here in your next reply.

Code:

************* Symbol Path validation summary **************
Response                         Time (ms)     Location
Deferred                                       SRV*C:\SymCache*http://msdl.microsoft.com/download/symbols
Symbol search path is: SRV*C:\SymCache*http://msdl.microsoft.com/download/symbols
Executable search path is: 
Windows 7 Kernel Version 7600 MP (4 procs) Free x64
Product: WinNt, suite: TerminalServer SingleUserTS Personal
Built by: 7600.17273.amd64fre.win7_gdr.130318-1532
Machine Name:
Kernel base = 0xfffff800`03052000 PsLoadedModuleList = 0xfffff800`0328ee70
Debug session time: Mon Apr 13 15:32:12.094 2015 (UTC + 9:30)
System Uptime: 0 days 0:42:56.888
Loading Kernel Symbols

First thing to do is update Windows 7 fully. These updates address lots of the instability caused by 3rd party drivers, so get that done as soon as you can.

Once Windows is fully updated, and you still get BSOD's, upload a freh zip file from DM Log Collector, and we'll take it from there.

On Mon 4/13/2015 9:55:18 PM GMT your computer crashed
crash dump file: C:\Windows\Minidump\041315-32682-01.dmp
This was probably caused by the following module: ntoskrnl.exe (nt+0x75C00)
Bugcheck code: 0x1E (0xFFFFFFFFC0000005, 0xFFFFF800030CAE84, 0x0, 0xFFFFFFFFFFFFFFFF)
Error: KMODE_EXCEPTION_NOT_HANDLED
file path: C:\Windows\system32\ntoskrnl.exe
product: Microsoft® Windows® Operating System
company: Microsoft Corporation
description: NT Kernel & System
Bug check description: This indicates that a kernel-mode program generated an exception which the error handler did not catch.
This appears to be a typical software driver bug and is not likely to be caused by a hardware problem.
The crash took place in the Windows kernel. Possibly this problem is caused by another driver that cannot be identified at this time.



On Mon 4/13/2015 10:55:10 AM GMT your computer crashed
crash dump file: C:\Windows\Minidump\041315-25755-01.dmp
This was probably caused by the following module: ntoskrnl.exe (nt+0x6F880)
Bugcheck code: 0x50 (0xFFFFF6D880015000, 0x0, 0xFFFFF800030812C8, 0x5)
Error: PAGE_FAULT_IN_NONPAGED_AREA
file path: C:\Windows\system32\ntoskrnl.exe
product: Microsoft® Windows® Operating System
company: Microsoft Corporation
description: NT Kernel & System
Bug check description: This indicates that invalid system memory has been referenced.
This appears to be a typical software driver bug and is not likely to be caused by a hardware problem.
The crash took place in the Windows kernel. Possibly this problem is caused by another driver that cannot be identified at this time.

2 more bsod's. I came back to the first bsod after I let windows update run then went to bed. I finished updating windows 7 fully so I tried playing LoL again then I got the second bsod.

Code:

*******************************************************************************
*                                                                             *
*                        Bugcheck Analysis                                    *
*                                                                             *
*******************************************************************************

Use !analyze -v to get detailed debugging information.

BugCheck 50, {fffff900e6bb8148, 0, fffff96000104cbf, 2}


Could not read faulting driver name
Probably caused by : win32k.sys ( win32k!TimersProc+73 )

Followup: MachineOwner
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Run a minimum of 8 consecutive passes, preferably overnight, or until errors occur using MemTest86+.

Reference:
RAM - Test with Memtest86+