Problem: After having been disconnected from power, even briefly, the iMac could not be turned on for several hours. Peeking through the bottom vent holes I could see that not even one indicator LED was lit during that time.
Secondly there was a rattling noise that I attributed to a broken fan.
Solution: Replaced the power supply. Turns out, that was also the source of the noise.

Obviously not following this guide, I opened my iMac that had full graphics failure, uninstalled the GPU-card, cleaned it, baked it in the oven to soften the solder and let the chip reattach itself, added new conductive paste, reinstalled it and it worked again.

I can't remember the temperatures, but there are tutorials to be found.

I picked the broken pieces caught underneath the stickers through the little hole from the outer side of the case with pointy tweezers.

I would caution against doing it from the outside only. The old feet are attached to a small ring on the inside. If you remove the foot from the outside, that little ring gets lost in the case and can potentially get into the fan.
I did not remove the stickers. Those actually caught the little ring and I could pick its pieces through the little whole with tweezers from a kit after ripping off the single original foot left on my machine.

Tutorial worked out well, and I followed all of the safety instructions. I also had a box of sand and a sturdy leather glove in reach, should the old battery start to act up. One cell was actually bloated a bit at age 9.

Glue removal under the battery and afterwards on the case was seriously laborious.

One clarification I would have liked to know beforehand: When removing the center two cells, the guide notes to watch out for the trackpad board. Additionally I would warn that you can slip under the metal cover that separates battery and trackpad. I did briefly and was worried when I realised.

10/10, would recommend for any tinkerer with less than 2 left hands.