Are you having both AVG and Microsoft Security Essentials installed? Keeping two antiviruses will cause conflicts anyway. AVG is a frequent cause of BSOD-s, please uninstall it with the >
AVG | Download tools and utilities. Do you have McAfee installed too?

It's a known cause to BSOD-s! Please uninstall it straight away >
McAfee Removal Tool - McAfee Uninstaller Code:
Start Menu\Programs\AVG Public:Start Menu\Programs\AVG Public
Start Menu\Programs\McAfee Family Protection Public:Start Menu\Programs\McAfee Family Protection Public
Uninstall this >
Code:
Start Menu\Programs\CleanUp! Public:Start Menu\Programs\CleanUp! Public
with the free version of
Revo Uninstaller (in advanced mode).
Reboot each time you uninstall something from the system.
Free up the start-up, nothing except the antivirus is usually needed.
Run the System File Checker that scans the of all protected
Windows 7 system files and replaces incorrect corrupted, changed/modified, or damaged versions with the correct versions if possible:
Run Disk Check on your hard disk for file system errors and bad sectors on it:
Recommended antivirus program for Windows 7 based on stability compared to others:-

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.
Let us know the results.