Reoccurring BSOD [ntoskrnl.exe] [hal.dll]

Hello and welcome acfourleaf as you have stated the dump ntoskrnl.exe fault can be a host of different causes and I see you have already done some of the preliminary stuff and I would like you to read my ditty and run what is in it - PART A: and post back snips of what you find.

Using HW Info
PART A:
You can test the volts on the PSU with HW Info HWiNFO, HWiNFO32/64 - Download < download the right bit version and close the right handwindow select Sensors and scroll down to the power section where you will seewhat the volts are doing see my pic. Now the section you want will be labeled -for example Asus boards usually have "Nuvoton" and Gigabyte boards"ITE" in any case the section you want will have Vbatt or VBAT in it(dead give away)
The original right hand window shows the machine running and is handy for thatbut for looking at the components in some detail close it and use the main lefthand side panel
FOR OTHER COMPONENTS
PART B:
Open each small square with + in it on the section the components are in andthen click on the individual component/s (it will highlight in blue) - in theright hand side will appear all sorts of details including brands speeds andother essential info that particular device. See pic for example.

I am asking because the PSU is very often overlooked as cause of problems in any machine and is one thing I liketo check first up.