My 3 years old hp f2105 got the prolem: the power

If this monitor has an external power supply "brick" like a laptop does then you need to test it for power output and replace it if needed. If it has just the typical PC power cord plugged into a 3 prong socket in the monitor it will be an internal power supply failure. About 3 yrs old is about the right time for it possibly to be bad electrolytic capacitors. If you have the skills to open the unit where you can see the internal boards (please unplug the unit while it's open to prevent electrical shock) you need to look at the little can shaped parts, usually with an X or K stamped into the top. If the tops are perfectly flat they are probably ok but if they are swelling up or are split and leaking a small brownish or whitish compound (dont wipe it with your finger, I have no idea what's in that leakage) then you have the problem - bad capacitors. You will need to replace them or have a shop replace them. Ideally the same uF (microfarad, measure of capacitance) and voltage rating should be used as well as the same size as most dont have much room but you can substitute with a higher voltage rating. If a capacitor is a 1000uF 25V you can use a 1000uF 35V but dont use a 16V. Many people have used close to the same uF rating and been ok but remember an electronics engineer specified that capacitance for a reason when he/she designed the circuit so it's best to use the same. Caps with both leads on one side, typical of board parts, are called radial and ones with a lead out of each end are axial. Places like Digikey, Mouser Electronics, Jameco and others have them listed by uF, V and size. Some more common ones are still stocked at Radio Shack but I prefer to use better quality at lower prices. If anything a local TV shop may have parts on hand they can sell you individually. Alternative is to replace the bad board as an assembly, or replace the monitor which is what the manufacturers want you to do so they sell more.