I have run a chkdsk and found errors on the OS before i made the post and with the new logs. Windows gadgets was one of the things repaired.
You may want to run this again to see if more is found. Hopefully not though.
HWInfo64 reports the hard drive S.M.A.R.T is all good.
I would probably run a short test and long test using the hard drive manufacturers testing tools. If they don't have one for your drive then you can use
SeaTools HDD Diagnostics.
Memory test has not been done. Should I use MemTest86 or a different tool?
Yes. That's what I would do.
Test RAM With Memtest86+
Please ensure you allow 8 passes of the program!
Download Memtest86+ here:
Memtest86+ - Advanced Memory Diagnostic Tool
Which should I download?
You can either download the pre-compiled .ISO that you would burn to a CD and then boot from the CD, or you can download the auto-installer for the USB key. What this will do is format your USB drive, make it a bootable device, and then install the necessary files. Both do the same job, it's just up to you which you choose, or which you have available (whether it's CD or USB).
Do note that some older generation motherboards do not support USB-based booting, therefore your only option is CD (or Floppy if you really wanted to).
How Memtest works (you don't need to read, it's only for those interested in the specifics):
Memtest uses algorithms (specifically two), namely moving inversion & what is deemed Modulo-X. Essentially, the first algorithm fills the memory with a pattern. Starting at the low address, it checks to see if the pattern was changed (it should not have been), writes the patterns complement, increments the address, and repeats. Starting at the highest address (as opposed to the lowest), it follows the same checklist.
The reason for the second algorithm is due to a few limitations, with the first being that not all adjacent cells are being tested for interaction due to modern chips being 4 to 16 bits wide regarding data storage. With that said, patterns are used to go ahead and ensure that all adjacent cells have at least been written with all possible one and zero combinations.
The second is that caching, buffering and out of order execution will interfere with the moving inversions algorithm. However, the second algorithm used is not affected by this. For starting offsets of 0-20, the algorithm will write every 20th location with a pattern, write all other locations with the patterns complement, repeat the previous one (or more) times, and then check every 20th location for the previously mentioned pattern.
Now that you know how Memtest actually works, it's important to know that the tests it goes through all mean something different. It goes from Test 0 through Test 12, many of which use either one or the other algorithm discussed above, among many other things.
Any other questions, they can most likely be answered by reading this great guide here:
FAQ : please read before posting