I have a cheap LCD that sometimes exhibits this problem (Chimei CMV 938D). For me, the most effective solution is playing with the brightness levels - it never whines at 100% brightness. I've always assumed it was the capacitors, though I've never been sufficiently motivated to take it apart and investigate.
It does seems to be temperature dependent - the brightness level at which it starts whining varies day to day, and how long it's been running, so I tend to just leave it on max.
I've had this screen for 2 years now, and it's done it since it was new, so while it might be an early warning of death, I've always just figured it was a function of a cheap build. Admittedly I don't often run mine in the brightness range where it whines.
Is the monitor under warranty? – Dave M – 2010-03-29T19:19:26.970
@DaveM The warranty status is not known at this time. :P – iokevins – 2010-03-29T20:27:34.253
Can you provide make and model? – Dave M – 2010-03-29T21:07:22.043
@DaveM It is an HP 1740 LCD monitor: http://h18000.www1.hp.com/products/quickspecs/12127_div/12127_div.HTML
– iokevins – 2010-04-01T20:25:36.340