Mac not powering up after power outage

Try booting into Safe Mode to see if that makes any difference.

Try booting the Apple Diagnostics to see if any hardware issues are detected.

Can you still boot into Recovery Mode (Command + R) or Internet Recovery Mode (Command + Option + R)?

Did you try running Disk Utility First Aid when you were at the recovery mode screen? Make sure to run First Aid on the hidden Container. Within Disk Utility of macOS 10.13+ you may need to click "View" and select "Show All Devices" before the hidden Container appears on the left pane of Disk Utility. Even if First Aid says everything is "Ok", click "Show Details" and scroll back through the report to see if there any unfixed errors listed.

What version of macOS is installed on this laptop?

Do you have the 13", 15", or 17" model? Retina or non-Retina model.

Sounds like the internal boot drive is corrupt or failing since even local Recovery Mode is not booting....that is when you use Command + R (if the internal drive is bad, then the internal drive may not appear so the system may resort to booting into Internet Recovery Mode instead).

Try booting into Internet Recovery Mode directly by using Command + Option + R so you can access the online utilities.

See if the diagnostics report any hardware issues. Unfortunately the diagnostics rarely detect issues. If the diagnostics do not report any issues, then I can provide instructions for creating & using a bootable Linux USB stick to check the health of the internal hard drive to confirm my suspicions. Just let me know. Or you can install macOS to an external USB3 drive and use DriveDx (free trial period) to check the health of the internal drive.

That picture of Disk Utility is showing just a 4GB size, but that may just be the volume. Did you click "View" and select "Show All Devices"? It isn't showing the physical internal drive. More than likely this is confirming a hardware issue with the internal hard drive, but hard to say for sure with that picture. Something definitely is messed up with that drive, I just cannot tell what.

Launch the Terminal app from the Utilities menu on the menu bar and issue the following command so we can see a better look at the drive layout:

diskutil  list  internal

That hard drive has failed since it is reporting incorrect information.

You can install macOS to a USB3 external drive in order to continue using the iMac since it is difficult to replace the internal hard drive on these iMacs. If you are handy, then you can try replacing the internal hard drive with an SSD....review the OWC upgrade options available and the installation videos OWC provides for your iMac. However, the Display Assembly is heavy & easily damaged if handled incorrectly (must be kept vertical or it can crack under its own weight), and there are several fragile easily damaged cable connectors which are difficult to reach and connect/disconnect. The videos make it look easier than it really is...some models it is even difficult with the display screws due to the magnets and how recessed these screws are.

OWC has official resellers in other regions as well:

https://eshop.macsales.com/shop/ssd/owc