Some electronics uses coils, transformers that can emit such a noise. Usually more annoying to the owner than any sign of impeding failure. A great technician could find it and use some spray shellac to glue the windings into place to kill the noise, but today's service costs will run about the price of a new monitor.

"Unpotted transformers can also get noisy. The iron laminations in the EI core start to vibrate. This is because the ?varnish? the transformer was usually dipped in has broken down due to the many cycles of expansion and contraction that takes place as the transformers have been turned on and off"
-> http://home.att.net/~chimeraone/vintagetransrebuild.html

You'll find such writings aplenty on the net.

Bob

Bob