Xbox one signing me out immediately after logging in, and cannot connect to Xbox live

I am afraid it simply says that it cannot connect to the wireless network straight up. Router has been reset as well.

I'd start with deleting your profile from the console.

Go to Settings -> Account -> Remove Accounts.

Then select your Gamertag. After that, try adding your profile back.

https://support.xbox.com/my-account/manage-gamertag-and-profile/add-remove-account-xbox-one

It might also help to change your password, and set up two-step verification (to rule out anyone else signing in as you on another console.)

https://support.xbox.com/my-account/microsoft-account/change-microsoft-account-password

https://support.xbox.com/my-account/security/turn-off-two-step-verification

After that, try restart the console by opening the guide going to settings, and then choosing "Restart console."

If you are still having problems connecting to Xbox Live, then go into the Settings -> Network and re-set up your connection.

https://support.xbox.comxbox-one/networking/network-settings

https://support.xbox.com/xbox-one/networking/network-connection-error-solution

Are any other devices having problems connecting to the same router?

Run the Xbox live test. Where does it fail?

Press the Xbox button to open the guide.

Select Settings.

Select All Settings.

Select Network.

Select Network settings. Any known outages will appear in the middle of the screen.

On the right side of the Network settings screen, select Test network connection.

Try performing a hard reset EXACTLY like this. Hold the power button on the console for 8 seconds or until the power shuts down completely.
Unplug the power cord from the back of the console for 5 minutes.
Plug the power cord back in and restart the console.