Blue Screen of Death on my laptop

Hello.

I have attempted to find a solution online without success... I am requesting assistance from the community.

My new laptop, purchased two weeks ago, is used strictly for League of Legends and YouTube. It has begun experiencing Blue Screens of Death several times daily. The system freezes or restarts automatically. It came with Windows 8.1 pre-installed. I have tried a system recovery and various driver reinstalls, but nothing has worked.
If anyone would be willing to review this and offer advice, here is the Whocrashed log:

System Information (local)
--------------------------------------------------------------------------------

windows version: Windows 8.1 , 6.2, build: 9200
Windows directory: C:\Windows
Hardware: Windows hardware : HP Pavilion 17 notebook PC , HP, 226A
CPU: AMD A8-6410 with AMD Radeon R5 Graphics, level: 22
4 logical processors, active mask: 15
RAM: 3690655744 total

--------------------------------------------------------------------------------
Crash Dump Analysis
--------------------------------------------------------------------------------

Crash dump directory: C:\Windows\Minidump

Crash dumps are enabled on your computer.

On Sat 20.9.2014. 10:46:57 GMT your computer crashed
crash dump file: C:\Windows\Minidump\092014-20015-01.dmp
This was probably caused by the following module: ntoskrnl.exe (nt+0x153CA0)
Bugcheck code: 0x1E (0xFFFFFFFFC0000005, 0xFFFFF80046766E10, 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 Fri 19.9.2014. 9:38:34 GMT your computer crashed
crash dump file: C:\Windows\Minidump\091914-20359-01.dmp
This was probably caused by the following module: ntoskrnl.exe (nt+0x153CA0)
Bugcheck code: 0x7F (0x8, 0xFFFFD000293A0130, 0xFFFFD000358F4ED, 0xFFFFF8010F56BD10)
Error: UNEXPECTED_KERNEL_MODE_TRAP
file path: C:\Windows\system32\ntoskrnl.exe
product: Microsoft Windows Operating System
company: Microsoft Corporation
description: NT Kernel & System
Bug check description: This bug check indicates that the Intel CPU generated a trap and the kernel failed to catch this trap.
The crash took place in the Windows kernel. Possibly this problem is caused by another driver that cannot be identified at this time.

On Fri 19.9.2014. 9:38:34 GMT your computer crashed
crash dump file: C:\Windows\memory.dmp
This was probably caused by the following module: ntkrnlmp.exe (nt!KeBugCheckEx+0x0)
Bugcheck code: 0x7F (0x8, 0xFFFFD000293A0130, 0xFFFFD000358F4ED, 0xFFFFF8010F56BD10)
Error: UNEXPECTED_KERNEL_MODE_TRAP
Bug check description: This bug check indicates that the Intel CPU generated a trap and the kernel failed to catch this trap.
The crash took place in the Windows kernel. Possibly this problem is caused by another driver that cannot be identified at this time.

On Thu 18.9.2014. 20:38:56 GMT your computer crashed
crash dump file: C:\Windows\Minidump\091814-36937-01.dmp
The issue likely stems from this module: ntoskrnl.exe (nt+0x153CA0)
Bugcheck code: 0x7F (0x8, 0xFFFFD0013C1A0130, 0xFFFFD0013C1C7FB0, 0xFFFFF80263F67EBF)
Error: UNEXPECTED_KERNEL_MODE_TRAP
file path: C:\Windows\system32\ntoskrnl.exe
product: Microsoft Windows Operating System
company: Microsoft Corporation
description: NT Kernel & System
Bug check description: An Intel CPU generated a trap that the kernel could not handle.
The failure occurred within the Windows kernel. It is possible an unidentified driver is responsible.

Your system crashed on Thu 18.9.2014. 17:52:19 GMT
crash dump file: C:\Windows\Minidump\091814-17187-01.dmp
The issue likely stems from this module: ntoskrnl.exe (nt+0x153CA0)
Bugcheck code: 0x26A5110A (0x1AC, 0x2, 0x0, 0xFFFFF80033118CAC)
Error: CUSTOM_ERROR
file path: C:\Windows\system32\ntoskrnl.exe
product: Microsoft Windows Operating System
company: Microsoft Corporation
description: NT Kernel & System
The failure occurred within the Windows kernel. It is possible an unidentified driver is responsible.

Your system crashed on Thu 18.9.2014. 17:13:02 GMT
crash dump file: C:\Windows\Minidump\091814-23484-01.dmp
The issue likely stems from this module: ntoskrnl.exe (nt+0x153CA0)
Bugcheck code: 0x3B (0xC0000005, 0xFFFFF801FC945B34, 0xFFFFD000A9D75500, 0x0)
Error: SYSTEM_SERVICE_EXCEPTION
file path: C:\Windows\system32\ntoskrnl.exe
product: Microsoft Windows Operating System
company: Microsoft Corporation
description: NT Kernel & System
Bug check description: An exception occurred during a routine transitioning from non-privileged to privileged code.
This looks like a standard software driver error rather than a hardware issue.
The failure occurred within the Windows kernel. It is possible an unidentified driver is responsible.

Your system crashed on Thu 18.9.2014. 16:33:50 GMT
crash dump file: C:\Windows\Minidump\091814-21250-01.dmp
The issue likely stems from this module: atikmdag.sys (0xFFFFF8012BEC80E1)
Bugcheck code: 0xD1 (0x4D5, 0x2, 0x0, 0xFFFFF8012BEC80E1)
Error: DRIVER_IRQL_NOT_LESS_OR_EQUAL
file path: C:\Windows\system32\drivers\atikmdag.sys
product: ATI Radeon Family
company: Advanced Micro Devices, Inc.
description: ATI Radeon Kernel Mode Driver
Bug check description: A kernel-mode driver tried to access pageable memory at a process IRQL that was too high.
This looks like a standard software driver error rather than a hardware issue.
A third-party driver appears to be the primary cause. You should try finding an update for atikmdag.sys (ATI Radeon Kernel Mode Driver, Advanced Micro Devices, Inc.).
Google query: Advanced Micro Devices, Inc. DRIVER_IRQL_NOT_LESS_OR_EQUAL

Your system crashed on Wed 17.9.2014. 22:59:55 GMT
crash dump file: C:\Windows\Minidump\091814-24203-01.dmp
The issue likely stems from this module: ntoskrnl.exe (nt+0x153FA0)
Bugcheck code: 0xA (0x436E75A8, 0x2, 0x0, 0xFFFFF80303B1C406)
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: Microsoft Windows or a kernel-mode driver accessed paged memory at DISPATCH_LEVEL or higher.
This looks like a standard software driver error rather than a hardware issue.
The failure occurred within the Windows kernel. It is possible an unidentified driver is responsible.

Your computer experienced a system failure on Wed 17.9.2014. 22:05:02 GMT
The crash dump file is located at: C:\Windows\Minidump\091814-22093-01.dmp
The issue likely stems from this module: ntoskrnl.exe (nt+0x153FA0)
Bugcheck code: 0x139 (0x3, 0xFFFFD0014C82D8E0, 0xFFFFD0014C82D838, 0x0)
Error: KERNEL_SECURITY_CHECK_FAILURE
File path: C:\Windows\system32\ntoskrnl.exe
Product: Microsoft Windows Operating System
Company: Microsoft Corporation
Description: NT Kernel & System
Bug check description: The kernel has detected the corruption of a critical data structure.
The crash occurred within the Windows kernel. This may be due to an unidentified driver...

Thank you in advance.

This is a pretty vague issue. Could be macOS, could be drivers, maybe even hardware... kernel errors aren't really a thing on their own, they just reflect whatever was running above them. Get a pro to look over those drivers and check your hardware. Hope you know someone who actually knows what they're doing...