Sorry to tell you...this isn't a problem with the monitor itself. It is actually a problem with your computer, it is crashing, bad.
I would say it's an overheating issue but usually that results in automatic reboots, but you are getting hard crashes, where windows suddenly dies and ends up just leaving anything and everything running. (I'm leaning toward the power supply) Meaning failing capacitors and after they heat up enough, they do not work right and end up outputting the wrong voltage or something like that.
It could also be your graphics card (as long as it is not onboard)
Another possibility is your RAM, you could have a defective stick of RAM, and after a while, as RAM fills up with programs and information, it then gets to the bad chip and errors out, windows crashes and leaves everything black.
It could also be a motherboard fault. Where maybe there is a VERY small fracture in the board from years of heating up, cooling, heating up, cooling...and repeat a hundred or so more times.
In conclusion, start with the power supply, by borrowing a known good PSU of the same wattage or greater.
Then if that doesn't fix it, try each stick of ram individually, if it still happens...
Try removing your graphics card and operating from the onboard graphics.
Failing that...I would say you are looking at a motherboard replacement
Hope this helps!