How do you reset a broken iMac?

If you have the cabling & another Mac, try...

https://support.apple.com/guide/mac-help/transfer-files-computers-target-disk-mode-mchlp1443/10.13/mac/10.13

If t mode works the iMac will be like an external drive that you can secure erase.

If you can boot into the recovery volume, boot into the Recovery volume (boot with the Command + R keys held down), you can select Disk Utility and erase the drive. If that works I wouldn't bother with reinstalling the system.

Of course if you want to get some files off of it beforehand follow BDAqua's recommendation.

Any luck yet?