Don't guess, have him shut the monitor and see if the whining goes away. If it turns out that it is the monitor it's possible it could be caused by the backlight or the inverter. My Samsung SyncMaster has a slight high pitched whine to it when it's turned on as do many other LCDs. That's normal.
The iMac G3 series have built-in CRT monitors. I've experienced whine problems with CRT monitors before and I know it's possible to eliminate or reduce the problem by using a lower refresh rate, but the Mac OS X display settings seem to have a single refresh rate per resolution and I don't think it goes low enough to be of any use. Last time I checked, it was set at 800×600 @ 95 Hz.
It could be the fan, the Hard Drive for two things. I have had some Hard Drives that put out a quite loud whine. Some worked for years, some were dying.
Is this Whine REALLY high in pitch? It could be from the Flyback Transformer (Horizontal Output Transformer). The really old Tray Load iMacs had a lot of Flybacks burn out over time due to heat. My 333Mhz Grape iMac blew out the flyback. Mine did not while but would spit every few minutes causing a flash on the screen till on day it shorted all the way out with a lot of noise. I yanked the plug and installed a new Flyback transformer and it's like new again.
How did you fix the flyback issue and what was the cost ? I fixed an old tray-load imac and within a few months the flyback went and I offered a refund or G3 tower as a replacement. They went with the tower and have been happy since. I have the tray-load in the basement, would be nice to get it running again.
If you are good with Electronics and soldering/Desoldering on PC Boards, you find the part number on your old flyback and search for a new one. It's been 3 years now I think but I found a seller on Ebay I believe with flyback for the older Tray Loaders and bought it from him for $25 or so brand new. It took me maybe an hour to take it apart, solder suck out the old Flyback and put in the new one. If you give me the exact specs of the iMac G3 I might be able to find one for you.