What do you do if your computer won't turn on after a power outage?

In your case it’s certainly the power supply is damaged. If you have some knowledge you may open the power supply and replace the main fuse with equal rate one inside the power supply.

If you are lucky the power supply may work again and your problem solved.

Mostly replacing the burnet fuse wouldn’t work specially if there were damaged components on the power supply, You’ll have to replace the whole power supply with the same rating power.