IMac Fan Revved Up All the Way - NOTHING Worked!

Question

Hi,
I've had a mid-2011 27" iMac (Intel) for about a year, and I am now facing the problem of having my CPU fan constantly revved up all the way (~4000RPM). I get this even when my CPU is 97% idle and the temperatures across the board (according to iStat) are perfectly normal.
Now, I've tried every possible solution I came across, and nothing worked. Among what I tried:
Resetting the SMC
Resetting the PRAM
Sleeping, restarting, shutting down, etc.
Re-installing Mountain Lion
Removing all sorts of applications and killing all sorts of processes
Using every imaginable fan control software (and I do mean /every/)
Formatting the hard drive and doing a clean install of Lion
Formatting the drive again and doing a clean install of Mountain Lion
For some reason, despite all the above "solutions" the fan still insists on revving up to above 3500RPM (usually the first few minutes or hours of running the machine after each of the solutions above works, but then the fan revvs up again for no apparent reason). In fact, the minimum CPU fan speed remains stuck at 3500 (even when I manual set it to, say, 1200, regardless of which fan control software I use).
So, do I have a hardware problem? Is it a problem with my temperature sensors? Do I need to get something replaced? My problem is that I'm currently living abroad, in a country with no Apple Store in sight, and hence no access to an Apple Genius. I really hate the idea of manually opening up my iMac and messing around with it. But is that the only option I have? Should I try to disable the fan, for example? If so, how? Check for loose wiring? What?
One final note that could be helpful: I noticed from the first or second week of using my iMac that its power supply makes a very faint buzzing sound when the machine is off (you have to place your ear next to it to hear it). Could this be a power supply issue, which hosed the temperature sensors over time?
Please help me with whatever suggestions you may have. Thank you.

Answer 1

I even tried booting off the Lion and Mountain Lion DVDs and can't find the AHT there either.
Since there aren't any Lion or ML DVDs provided by Apple, that's a strange comment. For the AHT failure, assuming that the machine came originally w/Snow Leopard, try this.
Mount disc 2, run this command in the Terminal app, OPTION-click & hold Finder's Dock icon, and select RELAUNCH:
defaults write com.apple.finder AppleShowAllFiles 1
That unhides all hidden files/folders.
Now, drill down to /"Applications Install Disc"/System/Library/CoreServices/ and drag the .diagnostics folder into your Lion or ML boot volume's /System/Library/CoreServices/ folder.
Run this command to hide the normally hidden files/folders and RELAUNCH the Finder again.
defaults write com.apple.finder AppleShowAllFiles 0
This should allow the machine to boot into AHT when restarting and holding down the D key.