From what you’ve described, my suspicion would be the power supply. It sounds like something is happening where it doesn’t completely shut down, but stops delivering sufficient power to the system. The fact that it’s a black screen and not a blue screen points toward it not being a ram problem, and unlikely to be your motherboard.
If you have a multimeter, you could check the voltages on some of your cables during normal operation and compare them to the readings you get the next time this happens.