iMac often crashes, sometimes it doesn't make it to the desktop

Hello,

I have an iMac in mid-2011 27 "3.4GHz Intel Core i7 16GB RAM and AMD Radeon HD 6970M 2048 MB and the following problem: If my iMac was switched off, it takes 10-30 attempts to start up. The process is always done by switching it off suddenly interrupted. With every attempt it boots a little further. When it is running, it keeps coming back to sudden crashes, strangely enough, but again more when it cools down (e.g. after hibernation) than under load. In the beginning it was when booting 2-5 attempts and only sporadic crashes 1-2 per day now I can hardly use it because it suddenly switches off 10-20 times a day during operation. As a test, I have now removed the display and no longer cause any errors or crashes, when using a second iMac as a monitor via the display port, I can connect all the connectors of the display except the narrow, golden ones (DisplayPort Data), then the crashes occur again.

I would now tap the graphics card, but it doesn't make sense to me why it then runs with the second Mac (Displayport) as a monitor without any problems.

The graphics card is also used here, right?

Previous measures:

1. PRAM reset

2. High Sierra reloaded.

3. Hard disks exchanged for SSD

4. Display exchanged

5. Power supply exchanged

6. SuperDrive exchanged

7. iSTAT installed (no abnormalities detected in the temperatures)

Unfortunately all without success so that only the graphics card, the logic board or the backlight board remain.

I would tap the graphics card if it weren't for the error-free operation via the 2nd iMac as a monitor.

Does anyone have a tip or a good idea here?

What should I swap next?

Can someone explain to me where the difference could be when using an external iMac (Thunderbolt <-> Displayport) as a monitor (is the graphics card used differently)?