I'm not sure what could be causing your problem, but my sister just had a problem with her laptop where she had a black screen. It started intermittently and seemed to be some sort of graphics issue. Sometimes it would boot up and you could see the Windows screen, other times there was nothing. I did some research for her and it sounded like her GPU (graphics processing unit) got fried. I also found out that her particular laptop was well-known to have this exact problem because it wasn't built correctly. There wasn't a proper heat sink.
Well, my sis took it to be repaired. I had told her about what I thought it was, so she mentioned it to the repair guy. He had it for a while and he thought it was the lcd screen that was bad. He ordered another screen, she waited and waited, and he finally got the new screen, and it didnt' help the problem at all. In the end, he agreed that it was probably an overheated GPU and said he couldnt' fix it.
In your case, it could be several possibilities. It could be as simple as a loose connection all the way to a hardware failure or impending hardware failure. I would also check the monitor to make sure that isn't causing a problem. My father just had a problem with his monitor that was happening more and more over time. It wasn't coming out of standby or was taking forever to come out of it. Then a few times there was no picture, just a black screen upon booting up the PC. You could hear it booting up with the Windows boot sounds, etc, but could see nothing on the screen. In this case, the problem turned out to be his monitor. I swapped it out with a new monitor, and that solved the problem. So I think yours is a matter of trial and error. Start with checking all the connections to make sure none are loose.