I own a 20" 1.8 GHz iMac G5 with 1 GB RAM. From bootup, it emits a constant humming/buzzing noise. It's not loud, but it's not quieter than a whisper either. The noise does not appear to be affected by the brightness level of the screen. The noise does not disappear when the hard drive spins down. It does not appear to be affected by the Processor Performance setting in Energy Saver Preferences, although the noise does seem to get louder sometimes when the processor is working harder.
I tried to isolate the noise from outside but wasn't very successful, so I decided to open up the back of my machine. The computer can be booted by pressing the top button of the two buttons to the left of the LEDs. Warning: I am not recommending this procedure to anyone; I'm just reporting what I did. I learned about the internal boot method from an Apple Discussion thread.
The noise seemed to be coming from the fan next to the hard drive, in the upper right-hand area of the computer. The hard drive itself did not seem to be creating the noise. In fact, when I placed slight pressure on certain parts of the fan casing, I was able to reduce or even eliminate the buzzing.
I wanted to take off the casing and look inside, or at least tighten the screws, but unfortunately, the screws on the fan are not ones that the user is allowed to mess with without voiding the warranty. And in any case, I did not have the proper tool to turn the screw, because it is not a regular phillips head.
It seems as though a solution to the problem wouldn't be difficult, but I'm afraid to report my findings to Apple, because the iMac user manual says that operating the computer when it is open or missing parts can be dangerous and could damage your computer. I don't think I need a new power supply or a new hard drive, and I've heard that midplane replacements almost never make the computer quieter.