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Configure the system to collect Small Memory Dumps (Minidumps) following this tutorial: Dump Files - Configure Windows to Create on BSOD
Avast! contributes in BSOD's often. As a test please remove it using its removal tool from here: Uninstallers (removal tools) for common antivirus software - ESET Knowledgebase
We recommended Microsoft Security Essentials from a strict BSOD perspective. Is most compatible & provides most stability compared to other antivirus app/Internet Security Software.
Do not start the free trial of Malware Bytes; remember to deselect that option when prompted.
Run a full scan with both (separately) once downloaded, installed and updated.
Make scans with the following:
-ESET online scanner
Perform a System File Check to check the integrity of all protected Windows 7
- Click Start Menu
- Click All Programs
- Click Accessories
- Right click Command Prompt
- Click Run as administrator
- and press Enter
Full tutorial here:
Check your hard drive(s) for errors by running chkdsk
Upload a screenshot of your hard disk using CrystalDiskInfo:
Make a hard drive test from the hard drive manufacturers website:
Number down items at start-up. Keep only your anti-virus, this also improves the time for logging into windows.
Take memtest. Run for 8 passes and test each stick in a know good slot for an additional 6 passes.
Pay close attention to part 3 of the tutorial in order to rule out the faulty stick.
Errors are sometimes found after 8 passes.
Do this test overnight, before going to bed.
Let us know the results and further BSOD reports.