How to turn an MBA on when the power button is not functioning?
Since you think it is a permanet damage the best option is to replace the keyboard.

If you are not sure it is a permanent damage and before you replace the keyboard consider this:

There is a tiny spring loaded contact under the key cap.

Sometimes (rarely) a food or dirt get stuck in there.

1- Use a air can and blow around it, hoping to blow out the dirt.

or

2- Use a Alcohol (with Computer in OFF mode) soak it, wait for 10-20 minutes.
Use Hair blower and warm it up to evaporate the alcohol (not to hot)

or

3- Buy new and replace the keyboard, it is not a walk in the park but doable. It might cost you aprox $60 for keyboard, and you will need a special screwdriver. Estimated TTC about 2 hours.