I did not want to pay for a logic board. Luckily, one of my colleagues wanted to sell her 2010 27 inch iMac. It is model 11,3, the one just before my 12,2 27 inch 2011 iMac. She bought it and used it as a paperweight for 5 years. It is in mint condition. It cost me less than a logic board! I transferred my solid state drive into it, and then migrated my stuff onto it. Works great! Theoretically it has a slower CPU, 3.6 dual core VS the 3.1 Quad core in my noisey faulty 2011 27 inch iMac. In use, I perceive no difference in speed. I wanted to keep the 2011 for parts, but it seems that the 2010 is different... Different logic board, LED screen connectors. The power supply looks the same and my extra bigger RAM chips work in the 2010. I might end up having to sell the faulty 2011 for parts...
My 27 inch 2011 iMac started to buzz like this after 5 years. It was silent for the first 5 years. Then the buzz started. I changed the PSU. The buzz came back after 2 days. Then, I changed the LED backlight board and the buzz came back after an hour... There is nothing left to change! WTF. If someone finds a fix, please let us know.