Hi poppi
You've had some bad luck over the last few months - computers can be very trying!
This link from one of our competitors comes up with a number of suggestions - and it involves a 27 inch iMac:
https://forums.macrumors.com/threads/27-imac-wont-boot-after-power-outage.1140241/
One suggestion that caught my eye was removing the power supply from the back of the iMac (with the power being switched off at the socket of course), leaving it for a few minutes, then pushing in and holding the power button for, say, 5-10 seconds.
Then replace the power supply to the back of the iMac first; then plug into wall socket, then switching on the power.
In effect, you are resetting the SMC; but this did seem to resurrect an apparently defunct iMac.
Have a look at the comments, anyway.
Good luck.
Ian