So after many months of my very intricate PC crash issue and many hours of arduous work to solve it, I'm going to summarize our measures and deliver an update of our progress:
1) We exchanged the old 650 W power adapter with a new 600 W power adapter.
This step was necessary because a sporadcic loss of power that lead to immediate PC shutdown. After some weeks we weren't even able to boot the PC, because the power adapter refused to supply energy.
Due to this measure we an conclude that the remaining issue of frozen screens (that always lead to a irreversible black monitor and sometimes to bluescreens) is not caused by the power adapter.
2) We reinstalled the Nvidia graphics driver
The bluescreen showed the error message: "nvlmddmkm.sys", which leads us to the Nvidia graphics driver. We found that the Nvidia graphics driver always crashed immediately before the frozen screens,
so we reinstalled the most recent driver clean a couple of times in protected mode and with your recommended tools.
This measure had no effect unfortunately.
3) We exchanged an old broken cooler with a new one
We monitored the temperature of all hardware components with speedfan. Due to a broken cooler the GPU and CPU temperature was a little higher beneath a burden with round about 70° C.
The new cooler lead to a significant decrease of temperature with 55° C.
Nevertheless there was no effect in frequency of crashes, the issue remained, so we can conclude that the issue is not caused by a heat problem.
Moreover we inspected and cleaned all components; we could exclude a dust problem.
4) We exchanged the graphics card.
A few weeks ago my old graphics card GTX 260 finally died. It was not possible to boot the Nvidia graphics driver any longer; there were screen distortions even in BIOS screen.
We exchanged the graphics card temporary for 2 weeks with an shitty ATI Radeon 5450. However, that measure finally worked, there were no further crashes in that period,
so we concluded that the broken graphics card must be the culprit for the frozen screens.
So I bought a brand new Nvidia GTX 1060, funnily enough the issue continued. Right a few minutes after integration the screen freezed with a bluescreen; error message: "nvlmddmkm.sys"
5) We exchanged the hard drive with a SSD
We conducted a memory (RAM) and a hard drive test with your recommended tool. All tests were normal, there were no issue found on the hard drive or memory, they seemed to be in a good shape.
Nevertheless it took 5-10 minutes to reboot the PC again after each crash, sometimes even the normal Windows desktop was not loaded with the message: "Windows is beeing prepared".
To speed up the PC I bought a 500 GB SSD. I can only recommend to buy a SSD; it was the best investment I've ever made in hardware, I'm on my desktop in less than 30 seconds now.
6) We reinstalled Windows 10 completely.
Since the issue started in April 2016 right after the update from Win 7 to Win 10, we concluded that something went wrong with the software update. This idea was supported by the observation,
that the ATI graphics driver worked, but the Nvidia graphics driver crashed (strangely).
So parallel to the integration of the SSD we reinstalled Windows 10 on the SSD.
Nevertheless the frozen screens (leading to a black monitor) remained, but there were no longer bluescreens. Even in event viever there were no longer entries that shows that the Nvidia graphics driver crashed.
I recieved 1 bluescreen once; that one differed from the others because it showed the Error: "VIDEO SCHEDULER INTERNAL ERROR"
So we can definitively conclude now, that the issue is not caused by the hard drive or a wrong Windows 10 installation.
7) Ultima ratio I decided to purchase a new mainboard, processor and memory.
The only remainig reason could be a broken mainboard, so I decided to replace my 10 year old components (ASUS P5N-E SLI mainboard, Intel Core 2 Duo E8500 2 x 3,16 GHz and 4 GB DDR2 RAM).
The new components will be the MSI B350 Tomahawk mainboard, together with the AMD Ryzen 5 1600 (6 x 3,2 GHZ) processor and a new 8 GB DDR4 RAM.
I will receive and install the new components this weekend.
Lets hope that the issue will be solved then
(If not I'm out of ideas; then you can feel free to write a doctor's thesis about that issue!)