Yes but we apparently ran out of tests. My MB has not integrated graphics so I couldn't do what you suggested.
However something even weirder happened.
The day after I did my last post with the crash dumps, the system began to crash already during booting.
I wanted then to boot in the safe mode and it crashed too (on the screen asking the PW after W7 has booted).
So as apparently the last option left was to send the GC to Gigabyte for exchange, I needed the Serial Number so I unplugged the power and removed the GC to read the SN.
After that mechanically and without thinking I put the GC back again, plugged power in and pressed the power button.
This time I had no crash but the BIOS wanted me to put a boot device what it shouldn't be doing. Entering the set up, I noticed that the BIOS options have been initialised - the list of HD, the booting order, the system clock etc. I don't know why but it looked like an initialisation so I put back the right HD to boot from and the system booted without crash.
Since that time and that is 3 days now, I had no black screens and no crashes in games or otherwise.
So my conclusion was that I didn't know why it was crashing and I don't know why it started working now.
As we did tests that excluded RAM, HD, drivers, temperature and the last (unvoluntary) experiment excludes apparently GC hardware, I don't know what's left as the possible black screen cause.
Hence it can potentially start crashing again in 1 hour or 1 week.
