Dual Monitor Setup

I have had a dual monitor setup for at least a year now with no issues on either monitor. A month ago, I decided to buy a new monitor and I set my wife up with my old monitor so she could use a dual monitor setup for herself. I plugged the monitors in and it booted up just fine. She went to work so she turned off her computer and went to work. When she came home that night, she hit the power button and all the lights and fans turned on and turned right back off which followed by it turning all the same things back on by itself and turning itself off. It did this about 3 times until finally, everything turned on and stayed on but there was no beep from the speaker like there usually is. There was no display on either monitor. On a hunch, I decided to unplug one of the monitors and turn it on and it booted up perfectly (had the beep and everything) and once windows prompted for the password, I plugged in the second monitor and both of the monitors worked properly. However, later that night when she turned the computer off again, all of the fans and lights stayed on and would not go off (we left it on all night just to make sure). When I woke up the next morning, the lights and fans were still on but there was no display or anything that could be done to prove that the computer was in sleep mode. Today, I finally decided to see if it was just the video card so I placed the video card in my computer and the computer booted up just fine with both monitors. Turned it off and turned it back on just to make sure and it still worked perfectly fine. Then I decided to try to swap the power supplies just to make sure that wasn't the issue. I put my power supply in her computer and vice versa and my computer booted up and turned off perfectly fine with her power supply in it. With my power supply in her computer, it turned on with no problem but when it came time to shut down, the lights and fans continued to stay on. When I tried to turn the computer back on, it did the same thing where the computer would not stay turned on unless one monitor is being unplugged. The one monitor is using DVI-D and the other monitor is DisplayPort. I've tried multiple different things but can't seem to figure out why this computer won't act right, especially since there was no issue with it before the second monitor was added. Any help would be greatly appreciated, especially since I'm probably going to start pulling my hair out pretty soon!

Specs:
Motherboard: ASUS P8B75-M
Processor: Intel Core i7-3770 3.40GHz
Memory: (2) Corsair PC3-12800 DDR3 8GB
Video Card: NVIDIA GeForce GTX 970

Did you try swapping the cables? Sometimes a cable can have a short or other flaw that can affect the overall electrical stability of the system. You also might try different monitors as well (swap the actual computers), since there could be something like a ground problem in the outlets her computer uses as well.

Another possibility is to upgrade the computers BIOS.

I haven't tried swapping the systems yet but will try that later but I feel like the cords are working fine especially since the computer will turn on with only one monitor and then once windows has loaded and it prompts for the password, I can plug the other monitor into the video card and it works perfectly fine. I've already tried updating the BIOS as well but that didn't work either

The only reason I mention is that grounding problems can cause all sorts of weird issues that you wouldn't think were related to that at all. Sometimes they can work fine under a certain load, but adding additional load causes the issues. I'm not saying it is the problem, but best to rule it out.