Neat tools to resolve Blue screen of dealth

I would use SFC /SCANNOW rather than chkdsk. As explained at https://www.sevenforums.com/performance-maintenance/325080-sfc-scannow-chkdsk-whats-diff.html the major difference: chkdsk checks disk for hardware issues. SFC is system file check and checks for missing or corrupt windows system files. Since the hard drive is brand new, I doubt that you would see a hard drive that is already bad. Besides if I'm remembering correctly your screenshot of speccy did not indicate that the SMART was tripped.

I would go to Window's System Reliability Monitor described in the CIO article here: http://www.cio.com/article/2998906/windows/how-to-work-with-windows-10-reliability-monitor.html

If you need any help interpreting BSOD (blue screen of death messages) I would suggest Nirsoft's Blue Screen Viewer, win crash report, and App Crash Report listed here:

http://www.nirsoft.net/utils/blue_screen_view.html

http://www.nirsoft.net/utils/application_crash_report.html

http://www.nirsoft.net/utils/what_is_hang.html

If memory is an issue, I recommend you look at http://www.howtogeek.com/260813/how-to-test-your-computers-ram-for-problems/

Other tools/resources

http://www.majorgeeks.com/files/details/wise_pc_1staid.html

https://technet.microsoft.com/en-us/sysinternals/notmyfault.aspx

http://www.majorgeeks.com/files/details/ultimate_boot_cd_(ubcd).html

Good luck and wishing you a speedy recovery