Well I share a similar problem with my second monitor, it began after I pull out the power connector out during usage. Now often there is a peep/whine coming out of it. You could try to RMA it during warranty, I have send back a laptop, two PSU's and a HD4850 because of this kind of sound so you'll prob get your approval. If not there is no other choice then let it be, and hope that it goes away with time. (unless your a LCD expert)
Maybe it does not go away after 10 Min, but you adjust yourself to phase out the sound. Hypersensitive hearing sucks, trust me
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