BSOD playing League of Legends, error 0x00000124

A stop 0x124 is a hardware error, but which prt of the hardware is failing is difficult to determine other than some tests and trial and error.

Test your RAM modules for possible errors.
How to Test and Diagnose RAM Issues with Memtest86+
Run memtest for at least 8 passes, preferably overnight.

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

Stress test the CPU.
Hardware - Stress Test With Prime95

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.

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

Are you overclocking? As you are getting BSODs, you should stop overclocking and run all the hardware components like CPU, GPU and RAM to their default settings. Also set the BIOS to default, too.
How To Clear CMOS (Reset BIOS)

If possible, plan to update the BIOS.

Code:

BiosVersion = F11
BiosReleaseDate = 05/17/2010

Get the version F12f, dated 2012/07/27.

I will also suggest to dismantle the computer and clean the inside carefully. Clean specially the air vents and fan grills. While Re-seating, apply thermal paste to the CPU.


Let us know when all are done.
____________________________________________________________________________________
BSOD ANALYSIS:

Code:

*******************************************************************************
*                                                                             *
*                        Bugcheck Analysis                                    *
*                                                                             *
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Use !analyze -v to get detailed debugging information.

BugCheck 124, {0, fffffa8006369028, b62a4000, 145}

Probably caused by : AuthenticAMD

Followup: MachineOwner
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2: kd> !analyze -v
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*                                                                             *
*                        Bugcheck Analysis                                    *
*                                                                             *
*******************************************************************************

WHEA_UNCORRECTABLE_ERROR (124)
A fatal hardware error has occurred. Parameter 1 identifies the type of error
source that reported the error. Parameter 2 holds the address of the
WHEA_ERROR_RECORD structure that describes the error conditon.
Arguments:
Arg1: 0000000000000000, Machine Check Exception
Arg2: fffffa8006369028, Address of the WHEA_ERROR_RECORD structure.
Arg3: 00000000b62a4000, High order 32-bits of the MCi_STATUS value.
Arg4: 0000000000000145, Low order 32-bits of the MCi_STATUS value.

Debugging Details:
------------------


BUGCHECK_STR:  0x124_AuthenticAMD

CUSTOMER_CRASH_COUNT:  1

DEFAULT_BUCKET_ID:  WIN7_DRIVER_FAULT

PROCESS_NAME:  League of Lege

CURRENT_IRQL:  f

STACK_TEXT:  
fffff880`02f6ca88 00000000`00000000 : 00000000`00000000 00000000`00000000 00000000`00000000 00000000`00000000 : nt!KeBugCheckEx


STACK_COMMAND:  kb

FOLLOWUP_NAME:  MachineOwner

MODULE_NAME: AuthenticAMD

IMAGE_NAME:  AuthenticAMD

DEBUG_FLR_IMAGE_TIMESTAMP:  0

FAILURE_BUCKET_ID:  X64_0x124_AuthenticAMD_PROCESSOR_CACHE

BUCKET_ID:  X64_0x124_AuthenticAMD_PROCESSOR_CACHE

Followup: MachineOwner
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Now go for the last part of my earlier suggestion. Dismantle the PC and apply new thermal paste.

If still the situation is the same, we will consider it that it is not failing due to heat, but the problem is indigenous of the CPU.

How old the HDD is?

Well, now wait and observe if your actions can reduce the situation down. Yes, if the cooling liquid is warm, it may cause the issue. And hopefully now it should work kinda better after cleaning up.

An old HDD will cause heat itself. At least back up your data externally for a safety reason.