Black screen but sound, no dump files

Hello,
My problem is that after I start to play any game, 10-15 mins pass and I have a black screen. There is sound, but the keyboard/mouse won't react, so I have to reset the PC - therefore there is no dump file. I really don't know what to do. Is there a software that monitors this kind of crashes?
Otherwise the PC runs for days on end if I don't use the VGA in games. This is my only problem with it. After restarting it, it usually runs in games all right, no crash later.
Thank you in advance for any help.

The VGA is a GIGABYTE GV-N970IXOC-4GD GTX970 4GB GDDR5 PCIE.

CPU : QuadCore Intel Core i5-6600K, 3933 MHz (39 x 101)
Mobo : ASRock Z170 Gaming K6 (3 PCI-E x1, 3 PCI-E x16, 1 M.2, 4 DDR4 DIMM, Audio, Video, Gigabit LAN)
Chipset : Intel Sunrise Point Z170, Intel Skylake-S

with VGA you mean the graphics card?

how old is your power supply unit (PSU)? and are you using a HDMI connector from GFX card to monitor?

Yes, the graphics card. I think it is the problem, because I have sound.

This is a quite new machine, I bought it this spring, brand new everything. I use a DVI cable.

Thank you for answering.