The power button on my monitor flashes but will not trun on

There is a chance that you may have a couple bad capacitors on the power-inverter board but more than likely the problem will be a shorted out transistor. There are 4 on the inverter side of the board and one set may have gone bad. Capacitor problems may have caused the transistors to fail. Transistors are probably c5706 or c5707 and are black with 3 legs going though the board.
You would have to open it up to check and would need an ohm meter to verify if the transistors are shorted out.