The power supply cord has a fuse that can be reset. Its worth trying otherwise you may need to buy a new one. Is it under warranty?
Some people think simply unplugging it will reset it. Not true.
To to do a full reset: unplug everything from the Wii. Controllers,Sensor bar,video cables, etc. Unplug power supply from the wall. Leave it for a minimum of 2 minutes.
Then in this order plug power supply into the Wii. Then plug it into the wall DO NOT USE A POWER SURGE PROTECTOR!!
See if the power light comes on. try to turn it on now.
If it does come on turn it off (power led red). Remove the power supply again from the Wii and from the wall. Wait minimum 2 minutes then plug the sensor bar into the Wii.
Now the power supply. Then plug it back into the wall directly.
If it comes on you can then re-add the video cables, controllers etc.
The key is to not use a power surge to do this.
And I forgot to ask Nintendo if I should never use a power surge protector or just to reset it. But I will ask and post their reply.
I had to also replace the battery in the Wii. I cant say whether or not that voids the warranty officially but when I sent mine in last month they didnt say anything and covered my repair costs (different matter).