Missing manual for Replacing GPU

We don’t have a Mid 2011 iMac GPU board guide. But this guide will get you mostly there Installing iMac Intel 27" EMC 2429 Dual Drive Kit (HDD or SSD) Follow it to Step 33. Finish removing the logic board out noting the cables you still need to disconnect from the backside. With the logic board out you can then remove the GPU and its heat sink.

Do make sure you apply a fresh coat of thermal paste on the GPU and replace the thermal pads on the V-RAM chips. Don’t use thermal paste on them as you need a special gapping paste which is not as good as the pads.

@roman78 - With the system back together what does the onboard diagnostic LED’s telling you? Locate in the upper right corner the LED’s

Here's a breakdown of the onboard diagnostic LED's:

• LED 1 - Indicates that the trickle voltage from the power supply is detected by the main logic board. This LED will remain ON while the iMac is connected to the AC power. The LED will remain on even when the computer has been shut down or put to sleep. The LED will turn off only if the AC power is disconnected or the power supply is faulty.
• LED 2 - Indicates that the main logic board has detected proper power from the power supply when the computer is turned on. This LED will be ON when the computer is turned on and the power supply is working correctly.
• LED 3 - Indicates that the computer and the video card are communicating. This LED will be ON when the computer is communicating properly with the video card. If LEDs 1 and 2 are ON and you heard the startup sound, but LED 3 is OFF, then the video card might be installed incorrectly or need replacement.
• LED 4 - Indicates that the computer and the LCD display panel are communicating. This LED will be ON when the computer is turned on and video signal is being generated. If the LED is ON and there is no image on the LCD display panel, the LCD display panel or inverter might be installed incorrectly or need replacement.
  

So what did you see?