Ensure the adaptor is the official Wii AC Adapter supplied for use with Australian consoles (Model No: RVL-002 AUS). 3rd Party AC Adapters or the use of an overseas version of the AC Adapter is not recommended. In addition disconnect any unlicensed third party devices which connect to the USB ports of the Wii or to the Wii AC Adapter.
Make sure the AC Adapter is plugged into both the wall outlet and the back of the console.
Most power issues with the Wii can be fixed by resetting the AC adapter. To complete this disconnect the Wii AC Adapter from both the wall outlet and the Wii console. The AC adapter must remain unplugged at both ends for a full 2 minutes. After you've waited 2 minutes, plug the AC adapter into the Wii system and directly into a wall outlet, not a surge protector or power strip. If the power light comes on and stays on, then it appears resetting the AC Adapter worked.
Try another Wii AC Adaptor; alternatively try your Wii AC Adaptor with another Wii console.