Random BSOD on Parent's new computer.

I concur. I would check your hardware like testing your ram, etc. and see what happens. Use a program called memtest 86+. Run several passes of that to ensure you get accurate results.

Code:

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Use !analyze -v to get detailed debugging information.

BugCheck 109, {a3a039d89cc1364d, 0, a3e8571e0f88735c, 101}

Probably caused by : Unknown_Image ( ANALYSIS_INCONCLUSIVE )

Followup: MachineOwner
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The .dmp files contain no useful information. Please run Driver Verifier for a minumum of 24 hrs or until the PC BSOD's - follow the instructions below carefully!

Driver Verifier - Enable and Disable

Driver Verifier will cause your computer to run very sluggishly - this is normal. What it is trying to do is force your system to BSOD and isolate the offending driver/s. When it does, reboot, disable driver verifier, reboot as normal and upload the new dmp file/s here.

I recommend creating a system restore point before turning on driver verifier:
System Restore Point - Create

If your system fails to boot to desktop once driver verifier is enabled, turn it off by booting into Safe Mode:
Safe Mode

You ran Driver Verifier for 24hrs without any BSOD?

OK. Ensure your system is up-to-date, including all 3rd party drivers. Please run the following and report back the findings:
Windows Defender Offline