Monitor's menu won't go away and the buttons don't work

As I am writing this I have this blue square on the screen with all the settings for this monitor. Whichever button I press on the monitor the menu won't go away. Not even the power button works, so that means I can't disable the monitor. Unplugging and plugging it back in doesn't work, as soon as the picture appears the menu appears as well.

Let me give you a bit of a history as it might help determine the cause.
About a month ago my old monitor (monitor 1) started behaving weird. It started turning itself off every now and again. Sometimes few times a minute. Every time it turns off it turns back on, with the splash screen saying "BENQ" and everything. I had no idea why it does that. I tried pressing the buttons on it to go into the menu but every button seemed to shut it off and every button seemed to turn it on. So I gave it to a family friend to try and fix it. He said that the "control board" started dying and that he doesn't have a spare one, or something like that. He then gave me a spare monitor of his (monitor 2) until I can buy a new one or fix monitor 1. So I took monitor 2 from him and sent monitor 1 to the shop so they can try and fix it. About a week passes and the shop calls and says that they fixed monitor 1. I go and pick it up and when I came home I unplug monitor 2 and plug in monitor 1. (monitor 2 was working perfectly then)
Monitor 1 worked for about 15 minutes and started shutting down again. And when I tried using the buttons they wouldn't work again. Same thing as last time. So I return it to the shop and tell them that it doesn't work. That was about a week and a half ago. They still didn't fix it. The problem is, now the monitor 2 also started having problems. It doesn't turn off yet but the menu buttons don't work. Power button doesn't work. Nothing. And on top of that the menu won't disappear from the screen. As I am typing this there's a menu on top of everything. Every now and again the menu will switch to a different option, like "brightness", "auto adjustment" and such, like the buttons are being pressed.

Now, I am wondering, could it be that my PC is "breaking" these monitors? Is there a way for a PC to physically damage a monitor? What should I do in that case? Also, I should say that ever since monitor 1 died and after I installed monitor 2 my PC has been getting blue screens of death. It hasn't happened once in 5 years, since I got this PC and it started after I got monitor 2. I don't know if that's something that's important but there it is.

If you need more info please let me know. I am trying to figure out what is happening and every bit of help is appreciated. Thank you.
 
Could you please provide some information, such as Make and Model of Monitors & PC hardware specs (to include make and model of video card or motherboard w/ integrated graphics and power supply).
Also have you in the past, or currently, overclock anything in your PC (GPU / CPU)?
Do you smoke or eat around your PC? I have seen buttons get "stuck" on monitors, then cause a shortage in the buttons, because someone had food particles on their fingers and pressed the buttons which caused food to get stuck in the little space between the button and the monitor housing.
 
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