No Power On at all

My monitor is a Gateway FPD 1730 and it was working nice until few month ago when it just refused to power on. The power led is lightind but I know that it doesn't mean much, and if it is quiet in my office, I can hear a very high frequency sound, but this is all is happening. I just want to know what could be the problem, how can be solved (repaired) and if it worth to be repaired

What it sounds like is the Power supply on your FPD is bad. If its making a High Pitch Sound, A circuit or piece of your power supply is failing. It would need to be replaced in order to get it working.

You can repair this easily if you have another FPD 1730 lying around that doesnt work you can replace parts, but its best if they were made around the same time because certain models have 3 boards(video board, inverter, power supply) But most have two boards (power supply, video card)
They are easy to replace and maneuver if you want to give it a try. Open the FPD and see what kind you have. If anything you might be able to find a part online.

Good Luck,
I hope this helps