Why is my 2012 iMac displaying a black screen and not loading despite the fan working?

Your 13 year old iMac has likely given up the ghost. A reputable third party repair shop may be able to bring it back but the problem is there is no source for parts so any repair would likely involved used parts IF they can be found.

The cost of repair may also be more than the iMac is worth. In my humble opinion it's time for a new computer.

Yup, it's had a VERY long run and ready to be sent to one of Apple's free recycling services.

Apple Recycling Programs

If you replace it with another Mac, simply follow the instructions in Setup Assistant and Migration Assistant to migrate to the new Mac.

HAËMHUK_Msk wrote:

The IMac fan works very quietly (I found out when I accidentally touched it, and it turned out to be warm at the back, created complete silence, began to listen to it and realized that it was working, ) but there is no reaction and loading, black screen. And 1 time the keyboard indicator lights up when you turn it on in the network and that's it. iMac 2012

[Re-Titled by Moderator]

If the fan is running, that just means that there is power from the power supply – and that other components are generating enough heat that the fan was switched on for thermal regulation; or that perhaps a tempature sensor has gone bad and the software has switched the fan on out of caution.

That doesn't prove that that everything else (like the GPU) is in working order.

If you have current backups – whether made with Time Machine, Carbon Copy Cloner, or SuperDuper! – you can use one of those as the source for Migration Assistant on a new Mac.

I don't know what you want to do about the internal hard drive.

when my 2011 imac did that it was because the gpu (video card) had fried

I recycled it after opening it and taking out the harddrive so I could salvage my data in the new mac I bought