I would suggest trying to pinpoint the problem as much as possible before spending any money. You already tried a different outlet known to be working, and I assume your surge protector is working if other devices work fine with it. Now your best (and cheapest) option would be to borrow a working Wii power adapter from a friend. If the Wii turns on then your power adapter is bad and it will need to be replaced. If your Wii still won't turn on after trying a known working power adapter, at least now you know for sure the problem lies within the Wii itself, and it will need to be repaired.
This happened to my Wii a couple of years ago. Wouldn't turn on for days. I tried different outlets, surge protectors... couldn't figure out what the problem was. I kept meaning to ask a friend if I could borrow a working power adapter to test it, but kept forgetting or didn't have time, so I just didn't touch the console for a couple weeks, and some time later I randomly tried plugging it in and turning it on, and it worked. I never did figure out what happened.
I had a power surge that blew the fuse in mine (in the plug). Be sure to replace it with a 3A one for safety.
there is no fuse in the plug
Just followed this advice and it works. It was taken out during a quick 4 power outages today. My motivated 11 year old found this post and now is the self-proclaimed king of research.
Thank you, scooter696971! This worked perfectly! Our power went out yesterday with a quick couple of bursts and then was out for about 3-4 hours. I did exactly what you said, and it worked great!