LCD gives irritating high-frequency sound !

Probably the SPMS. Takes more than soldering skill to troubleshoot those and they do have some lethal voltages.

errrp SMPS :)

thanks, but what is the SPMS and how does it look like?

Also how can I safely remove the high voltages without damage the electronics or me ;)

The SMPS is a "Switch Mode Power Supply",it may be "internal" to the monitor,or it might be in the little "power pack" for it (varies by model.My monitor has it internal -no "power pack".)

You can generally tell the SMPS section by the small ferrite transformer,and a large capacitor (400V,100uf,perhaps.) *Discharge that capacitor before you even think about poking around inside!* (don't short it out though!) High voltage hurts,at the least..and worst case,can be !LETHAL!

Another possibility is the CCFL inverter for the backlight. Again,High voltage on the output side (the side that goes to the backlight tube(s).) There is likely a small 2KV 100-1000PF capacitor in series with the lamp(s)..you might want to discharge it also (short it with a screwdriver -DO NOT use this trick on larger caps -big BANG,and lots of sparks!)

Those are about the only possible sources of 'whine' in an LCD monitor,that I'm aware of.