Hi!
It can be multiple things.
The two most likely issues:
First thing: Overheated.
Second thing: Power supply is bad.
To solve the power supply, please replace this one first and see how it goes. It's way easier to just replace this one and see if it works or not.
To solve the overheating, you need to open up the Wii and remove all dust, also clean the fan thoroughly. After this is done, you can replace the thermal pads under the heatsink. Little note: Usually you don't need to replace it, but if you are having issues, it is recommended to replace it.
Guide: [guide|3458|Nintendo Wii Heat Sink Replacement - iFixit Repair Guide|new_window=true]
Please let us know if you need any more help! Good luck!