IMac 2012/2017 won't turn on after power outage

Hello,

This is already the fourth time I'm struggling to turn my iMac (2012-2017 model) back on after a power outage. When I try to turn it on and press the button, there's no noise, no light, no fan sound, nothing...

The last times, I somehow managed to eventually turn it back on by unplugging the computer and plugging it back in multiple times, blowing into the screen's connectors, pressing the power button normally or for a long time... The procedures mentioned on Apple's website (pressing the button for 10 seconds then pressing normally) or resetting the SMC (unplugging for 15 seconds, plugging back in, pressing the button after 5 seconds) have never been successful.

Yet it would eventually turn back on after many random attempts, with one instance where it powered up by itself after being plugged back in, without me pressing the button.

But this time, none of my attempts are working :( The status of the screen connector is okay, but upon inspecting the power connector, I noticed that the tips of the prongs were damaged/altered (see photo). Could that be a factor?

If not, do you have any other ideas on what I could do to try to revive it?

The thing is, if some parts are dead, how come it was working before?

Thanks in advance to anyone who can give me advice!