Monitor will not turn on including power switch
I suspect the power supply for the monitor. Try a power supply from a working monitor. If you have a used computer store nearby, take your power supply to them and try it on another monitor.
There is no need to turn off a monitor using its power switch. Monitors automatically go into standby mode when they are not receiving a signal. In standby mode they use less than one cent of electricity per day. If saving electricity is your goal, raise the temperature in your home by a degree and run the air conditioning less.