BSOD randomly while browsing

The crash is a 0x24 what refers to problems with the Windows File system / hard drive.

Diagnostics Test

 HDD TEST

Run SeaTools to check the integrity of your HDD. SeaTools for DOS and Windows - How to Use - Windows 7 Help Forums
Run following tests

1. Short Drive Self Test
2. Short generic
3. Long generic

If the short generic fails, no need for the long generic.

   Note

Do not run SeaTools on an SSD as the results will be invalid.

Run chkdsk
Disk Check - Windows 7 Help Forums

Run HDTune to

• scan for errors, no quick scan but full scan
• check the health,
• benchmark.

It may take some time, but please take the time you need to perform it properly.
Let me know what the results are

• of the error scan,
• make a screenshot of the health of every hard drive and post the screenshots,
• post screenshots with the benchmark of the
  
  • transfer rate,
  • access time,
  • burst rate,
  • cpu usage.

Diagnostics Test

 System File Check

Please try following:

• Open an admin command prompt
• Copy/paste "sfc/scannow" (without quotes) and press enter
• When it finished reboot your system
• Open again an admin command prompt
• Enter sfc/scannow again

If sfc/scannow says "Windows Resource Protection found corrupt files but was unable to fix some of them" after the second SFC, please upload the cbs.log file located at {windows partition}\Windows\Logs\CBS\, if the file is too large try a 3rd party uploader like dropbox, onedrive, google drive, mediafire etc.
System File Check(SFC a.k.a. Windows Resource Protection) needs to have your system rebooted in order for sfc to try to fix the problems that it finds.