My fans are spinning on full speed without any reason

Reset the SMC again. Do it 2-3 times and follow the instructions to the letter. Unplug from the back of the iMac not the wall.

1. Shut down the computer.
2. Unplug the power cord from the back of the iMac.
3. Wait fifteen seconds.
4. Attach the power cord.
5. Wait five seconds, then press the power button to turn on the computer.

Apps can affect Mac performance, battery runtime, temperature, and fan activity - Apple Support

Please start up in Recovery mode. Same?

Then you need to run the Apple Hardware Test Using Apple Hardware Test - Apple Support or have you already tried that too? 😠

I don't understand your response. The question was whether the fans run at full speed in Recovery mode. Do they?

Your iMac shipped with Snow Leopard on a gray two dvd install set. If you don't have those discs you have a couple options.

1. Order a replacement set of original install discs from Apple.

2. See if you can find the correct version of AHT here https://github.com/upekkha/AppleHardwareTest

3. Try this trick to run AHT without a disc. I have not tried it so I can't confirm that it works.

How to run AHT w/o the system discs

1) SHUT DOWN the computer (Don't RESTART... shut it down)

2) Hold down the OPTION + D keys

3) Press the Power Button (make sure to hold down the OPTION + D keys first)

4) Continue to hold down the OPTION + D keys until the system enters AHT mode

5) Let the app verify the hardware setup before initiating the test.

6) There are two testing modes. To select the "Extended Test" activate the check box below the Test button.

I'm going to leave this to Linc Davis as he's much more well versed in OS X than I. Good luck.