Hi JR and welcome.
The same problem with 3 monitors on the same PC suggests to me something wrong with the computer's graphics solution (card or on-board), or a common cable, but not the monitors. You are describing a classic "graphics card" problem - where the card is failing to send a "wake up" signal to the monitor.
Do other monitors behave properly on this computer? Have you tried those monitors on different computers?
That said, I did find where someone else with the same monitor had the same problem. The suggested solution was to press and hold both left and right arrow buttons for 1 minute, forcing the monitor to change inputs. 1 minute seems excessive to me (4 - 5 seconds seems more likely - if this input mode change feature is actually a design feature), and the OP never responded to say if it worked or not. So I am not sure of the suggestions validity.
If other monitors work fine on that computer, then that would indeed point to the monitors. If you have 3 of the same model monitors (or same model anything) an all failed the same way, I would probably contact the company. Maybe there's a recall you missed.
As for which component, there are probably dozens in the circuit(s) that control the monitor's sleep, wake and handshaking tasks. There is no way anyone could tell via a forum which specific device failed. It needs at least a hands-on visual inspection of the monitor's innards to look for something that got too hot. Ideally, you would need to take it to a technician who has the necessary tools, skills, training and tech data to troubleshoot. Also, as a technician, I can tell you that a failed device (failed resistor, for example) in the wake circuit of Monitor 1 does NOT suggest the same resistor failed in Monitor 2 or Monitor 3. A fried resistor just means there was too much current in circuit - cause unknown and the resistor could not handle it. It could easily be an associated device in the same circuit that failed first. Certainly the same circuit is suspect, and the resistor might be the first place to look, but each monitor would need to be troubleshot separately.
At the same time, again as a technician, with 3 failed monitors, I would be hesitant to connect yet another monitor to that computer. I would need to confirm and know for a fact the computer's graphics solution was not destroying these monitors before risking yet another monitor. Not sure how a home user could that except by replacing the graphics solution by installing a different card.