Unfortunately, the power supply is internal to the monitor and this is the likely problem. 
It is of the 'universal' input type that is compatible with a range of  90-264 VAC 50/60 Hz indicating that it is a 'switched mode power supply' and these have a design problem that makes the reliable operation of the supply doubtful unless a certain weak point (electrolytic capacitors in the feedback path) is properly attended to.
The run-of-the-mill capacitor in this useage is subjected to high ripple currents which can cause a cheap capacitor to chemically break down, dry out and then finally fail to pass enough signal to keep the supply running or enable it to start up.
 
If you are adventurous, you can open the monitor, examine the components near where the AC power cord terminates and look for vertically mounted, cylindrical parts with shrink wrap bearing the values and an exposed, scored, aluminum top.
Sometimes, the top will bulge or the base at the board may show signs of crystalline deposits.
If you find no parts that appear as described, the alternative is to find a tech who owns a capacitance meter with DF (loss) function. So equipped, the failed part is fairly easy to find. 
The values of these parts will lie between 4.7 to 100 uF with voltage ratings of 6 to 35 VDC.
Defective parts need to be replaced with special capacitors that are rated for high frequencies with low losses. These parts cost a few pennies more and most companies don't seem to care about the eventual failure of the inferior parts since it will typically happen after the warranty expires.