Why my xbox 360 s is not connecting to xbox live?

ok so does anyone know why my xbox 360 s cant connect to live using wifi but the one that has an Ethernet cord can?? and no its not a moden, ip, or port forwarding problem

Is there a reason why I can't sign in to my account and Connect t Connect to Xbox live on Xbox 360?

The games are all digitally owned in my library. There are no discs. I had no troubles with this on my original Xbox One that recently broke and required me to buy a new Xbox One S. The emulator I am referring to is the internal emulator that all Xbox
Ones run when playing a 360 Backwards Compatible game. When I install a 360 game and try to run it on my Xbox One S, the game will load HOWEVER I cannot connect to Xbox Live while in the 360 emulator. Due to a recent troubleshooting that suggests uninstalling
the game and clearing 360 cache and profiles, I would need to redownload my xbox live profile for the 360 emulator ON the One S. Since the emulator WON'T connect to Xbox Live, despite my Xbox One S BEING connected to Xbox Live, I cannot download my profile
and therefore cannot play and save my progress. I've tried with multiple games but they all give me the same issue of being "unable to connect to xbox live". I've tried all of the Mass Effect games, the Dragon Age games, Star Wars: The Force Unleashed games,
Banjo-Kazooie, and Fable series of games and NONE of these will allow me to connect to xbox live.

No i dont, it is a xbox 360 S

Internet is connected it shows it

Only thing that isnt i connected is xbox live

My xbox box gold yearly subscription shows it is active On mricosoft.com

It's refurbished.

Also Xbox One will have 300,000 Xbox Live Azure servers as suppose to Xbox 360's 15,000 Xbox Live servers world wide. This is why many ADSL2 broadband players have experienced some multiplayer issues with Xbox 360. It's because there are only 15,000 servers
world wide for Xbox 360. When I download stuff on my PC, it's way faster than on my Xbox 360 Slim console because Xbox 360 has only 15,000 servers world wide. Xbox One's 300,000 servers should offer more fluid connection even for those of us on ADSL2 broadband
speeds.