Mac Book Air not turning on

You can try a new MagSafe adapter (make sure you get an Apple genuine unit): Power & Cables - Mac Accessories - Apple, however, this may be a hardware issue with the MacBook Air itself.

Perhaps instead of buying a new adapter, you should first take your Mac to Apple to see what they say. Get started by finding a nearby Apple Store, Apple Store - Find a Store - Apple, then schedule an appointment at the Genius Bar: Get Support.

If there is not an Apple Store near you, then see if an Apple Authorized Service Provider is: Get Support.

Jack

Welcome to the Apple Support Communities.

Please take a look at If your Mac doesn't turn on - Apple Support.

When your MagSafe cable goes amber, that means it is charging your MacBook's battery. Wait a while and see if it turns green. If needed, you can refer to: If your MagSafe cable or power adapter isn't working - Apple Support.

Jack