BSoD while playing League of Legends (ingame)

Security App

• Start Menu\Programs\Norton Internet Security

Crashes indicate Norton being a possible cause. Remove Norton and replace with Microsoft Security Essentials to see if it provides more stability. Uninstallers (removal tools) for common antivirus software. Microsoft Security Essentials and Malwarebytes are recommended from a strict BSOD perspective. They do not cause blue screens on the system as other AV products do.

Microsoft Security Essentials, Free antivirus for windows and Malwarebytes Anti-Malware Free

   Information

• Do not start the free trial of MalwareBytes, unselect that option when prompted.
  
  
  
• Update and make full scans with both separately.

Start up
Keep less stuff at the start-up. Only anti-virus, this helps avoid driver conflicts and improves time to log in to windows.
Troubleshoot a Problem by Performing a Clean Startup in Windows 7 or Vista
How to Change, Add, or Remove Startup Programs in Windows 7

Kaspersky TDSSKiller - How to remove malware belonging to the family Rootkit.Win32.TDSS (aka Tidserv, TDSServ, Alureon)

ESET online scanner - One-time virus scanner free with ESET online scanner

Hard Drive/Storage
Post disk summary using CrystalDiskInfo software: CrystalDiskInfo Standard Edition

• For how to upload a screenshot or file, read here

Make a hard drive test from the hard drive manufacturers website: Hard Drive Diagnostic Procedure

Disk Check
For errors on your Hard drive(s): How to Run Disk Check in Windows 7

System Temperature

Ensure that there are no heat issues, For monitoring heat of the system use Speccy or HWMonitor

SFC /scannow to check windows for corruption:

How to Repair Windows 7 System Files with System File Checker
1. Click Start
2. In the search box, type Command Prompt
3. In the list that appears, right-click on cmd.exe and choose Run as administrator
4. In the command window that opens, type

sfc /scannow

and hit enter.

This tutorial USB Selective Suspend - Turn On or Off may help you:

To Disable Selective Suspend:
1. open the control panel
2. go to power options (you may have to set view to small icons)
3. click change plan settings
4. in the window that opens:
5. click change plan settings
6. click change advanced power settings, expand usb and ensure usb selective suspend is disabled.

Memtest86+
Run Memtest86+ for at least 8-10 passes. It may take up to 20 passes to find problems. Make sure to run it once after the system has been on for a few hours and is warm, and then also run it again when the system has been off for a few hours and is cold. How to Test and Diagnose RAM Issues with Memtest86+

   Note

Pay close attention to part 3 of the tutorial in order to rule the faulty RAM stick out.

   Tip

Do this test overnight.

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Thanks for the update :)