The chassis in all monitors are getting pretty old and tired.
The sound you hear is the sound of the switching FET in the power supply attempting to start up. it's failing to start because the FET has an overload protection built into it.
The capacitors are dried out and being an extra load. the load is too much for the FET and and power supply shuts down. it waits a little bit and attempts to start again. over and over.
dweet dweet dweet dweet. or chick chick chick chick. or wub wub wub wub. all kinds of different sounds from different FET manufacturers. sometimes fast, sometimes slow.
but yeah, you'll need to replace the capacitors on the chassis with some new ones. basically all the bigger electrolytic capacitors... don't worry about the little tiny ones or the plastic dipped ones.