That is the noise of my CRT monitor. Google informed me that perhaps melting silicone over the coils (?!) will help dampen the sound. Either that or putting it in a wooden carpeted box with a glass front. Does anyone else have any suggestions, or thoughts on the two I listed? Is it possible that my monitor is slowly melting and will one day explode in my face?
The noise is not indicating that your monitor will explode
You even acknowledge that the noise has been present for a long time, just drowned by fan noise.
My own CRT (HyundaÃ¯ V770) emits two different noises : one high pitched, that is related to the power unit of the CRT and the other one, more of a buzzing, that has the same frequency that the refresh noise and change with it. It's probably related to the electron gun and the process of drawing the image on the screen.
About the possible solutions, that's the first time that I hear about this closed box idea. It should stop these noises from bothering you, especially the high pitched noise. But CRTs emits some heat (reason why there are little openings on their upper side), my 17" CRT draws 70W according to manufacturer data and I suspect very little of it is dissipated through the light emitted by the screen. In a enclosed box the heat will build up very fast, so beware of not cooking it.
The glue gun on coil is fine for a PSU but for a CRT it gets trickier as you can't easily access the electronics, let alone find the culprit. I once tried to open my screen, it was such a mess with the metal casing that I gave up.
I convinced myself to get accustomed to it as these noises are not very obtrusive and they are somewhat mixed with a faint PSU fan noise.
Flat screens should be devoid of the buzzing noise, but anyway some also have the high pitched noise judging from the forum posts here. It makes sense as being a TFT or CRT you still have to convert the power coming from the wall at some point, even though some TFTs have a stand alone power converter that you can hide under the desk.
Maybe you can experiment a bit with the surrondings of the screen and your sitting position. I noticed strange reflecting of the high pitched noise on the wall near me, and as with every interference, in some place they will interfere constructively and in some other place destructively, resulting in less noise bothering you.