In my experience, BSOD is most commonly related to drivers, and specifically, video drivers. However, the corrupt HDD does catch my attention because that would not be a typical result of a failed gfx card. It could potentially damage its PCIe slot though.
First thing is to try reseating all connectors (HDD, RAM, PCIe cards). If youve already tried this, or it fails, I would start narrowing down the possibilities, beginning with the gfx card. Remove it and use the on board graffics. If this works, concentrate on drivers. If fail, test any other PCIe cards in similar fashion. If fail, remove all but two sticks of ram. If fail, swap the RAM with different modules. If fail, try a fresh OS install on a separate disk. If this works, it was a software issue on the prior installation. If fail, you may have a bad motherboard.
I once had DIMM slot 1 die on a mobo, and as a result the rest of the RAM would not initialize properly. I blamed it on a capacitor that looked extra bulgey and moved on to new gear. Good luck.
In response to Update#3
This screams video driver issue. Possibly a 3D/DirectX/OpenGL config somewhere. Make sure DirectX is up to date and check out the dxdiag tool. Try different/older versions of the driver, newer is not always better.
The most likely cause of this type of crash is defective memory. As suggested by harrymc, the first thing to try is generally to run a memory testing program, such as Windows Memory Diagnostic (included in Windows), the original MemTest86 (maintained by PassMark Software), or the open-source Memtest86+. (I've added this section for the benefit of other readers here who may be experiencing similar problems but not have tried memory testing.)
The question author can skip this section. It is being retained for reference by other readers.
If the memory test passes, you may have a faulty processor.
The processor's integrated memory controller (IMC) can sometimes cause memory problems. Simple memory operations like reading data from particular memory locations may work normally, but the processor's ability to perform essential memory management operations, including virtual memory, aren't tested by memory testing programs.
Another possibility is a faulty cache. Caches are small amounts of memory inside the processor used to accelerate memory accesses. Although your processor should be able to detect cache errors (and generate a machine-check exception when that happens, causing a WHEA_UNCORRECTABLE_ERROR
BSOD), it is not impossible for data in cache to get corrupted and cause memory corruption without the processor itself noticing. That, too, would not be detected by memory testing software.
To check the IMC, download Intel's processor diagnostic program and run an IMC test. To check the processor caches, download Prime95 and run the small FFTs torture test (your processor may get very hot or the fans may run loud; this is normal). If either test fails, you'll probably need to replace the processor. (I'm assuming the processor and memory are not overclocked or otherwise being operated outside of specifications.)
Since you've run a memory test and have found errors, it should be pretty obvious that one or more memory modules need to be replaced. I can glean more information from the report you've posted.
The errors occur at one particular region of the memory, around 0x19BDD79F0, which would limit the problem to one module. The address suggests, but does not confirm, that the problem is in one of the Patriot Memory modules.
Because memory on most systems, including yours, works best in pairs, try removing both modules of either brand and rerun the test. If that doesn't work, reinstall the modules you removed and remove the other pair. If the problem clears up, you can use the system normally until you get replacement memory modules.
I should note that Windows 10 uses more advanced memory management techniques, including virtual memory compression to maximize performance on systems with limited memory. Although your system has 16 GB of memory, Windows will still compress the data in memory by default (my desktop has 32 GB and is no different here). Memory errors are detected readily during compression and decompression of data and will immediately cause the operation to fail, causing the system to crash. Memory errors affecting uncompressed application or other data would "simply" result in application crashes or corrupted files (though it can still cause OS crashes). For this reason, Windows 10 is more sensitive to memory errors than previous versions of Windows.
Best Answer
1) Check your memory dump with Windbg. (may not help in this case)
2) Check both sticks, one-by-one, not just two of them together.
3) Check the memory thing with Prime95. It can stress memory.
Your PSU may also play a role in this. Especially if you run into BSODs while you do intensive tasks.
Try getting a second one and test stabilty with that.