problem with consoles connectivity

Can you please provide the exact error code? From the information gathered, it sounds like you are having issues accessing the xbl servers, if this is the case, it most likely will need to be fixed on microsofts side. However you could try the following:
clear your cache and marketplace data from your harddrive, reboot your rooter and/or run a network test and look at the values returned (by pressing y for status afterwards).

Hello, My name is Jesse. I'm an Independent Advisor and a member of the Microsoft community and I'd love to assist you today.

Unfortunately we are not allowed to assist with self repair of Xbox devices as it violates the Microsoft TOS. I'll suggest you take the console to a professional to figure out what's going on

I'm Samy an independent advisor. Welcome to the Xbox community. How are you?

Your console is connected to the internet, right?

Disconnect from your current connection and remove any disc that is in the console.

Press and hold the console power button until the console turns off, remove the HDMI cable and power cord from the console for about 1 minute. After 1 minute plug everything back in, turn on the console.

After turning on the console, share your phone's connection with the console as a hotspot. Once connected, put the disc in and see if it solves the problem.

If the problem persists, I'm afraid it's a problem with the console's disc reader.

The problem maybe is in the connection, the console you keep connected with the WiFi or with the Ethernet cable?

Hello .

what can be the problem that is not connected to xbox live my console , but it is connected to the internet?