This issue is mostly caused by the power source.
This can happen to old power sources, 3-4 years old.
Another thing that you can check is to switch the monitor cable to the integrated video card, if you have such thing. But usually if your PC has worked before from the dedicated video card jack and now is not, most definitely is the power source.
Other things. If you hear beeps, check the RAM memory. If nothing works, you can eventually try to reset the CMOS (the BIOS jumper). Check your motherboard’s manual in order to locate the CMOS jumper.
But overall, the first thing that you need to do is to try to replace the power source and see if the monitors will run with a different power source.