xbox live connection shows that it is working but cannot connect

As stated in my first post, i've tried already conencting only my console to router, i've tried even connecting my console directly to ISP cable (without router) - testing shows that console is connected to internet, but cannot connect to the xbox live.

"Yet, when you attempt to connect it immediately shows that message that you cannot connect? No problem! "

My console already after start shows that it is not connected to the xbox live, and after test, well... testing works normally, just after last step it shows that it cant connect to xbox live. For results of 3rrd step i need to wait few (10? 20?) seconds,
if that's what you mean.

Not to say, i've tried creating new account, or anything related to xbox live (like downloding my profile, updating console etc), and nothing works.

Hey there, have you signed into your account on the PC and verified the information in your Microsoft account. For example, verify the billing information or the information in the Password and security info section, which could be your security proofs:

support.xbox.com/.../error-code-800704dc

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There is also more information on adding and verify security proofs here:
support.xbox.com/.../add-security-proof

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If you're sure that's all verified then delete the profile from the console (profile only), clear the system cache 3 times. Restart the console and re-download your profile.

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Delete and re-download profile:
support.xbox.com/.../profile-move-delete

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Clear system cache:
support.xbox.com/.../clear-system-cache

I too am having the same problem you are started 2 days ago

Same problem here too! Won't let me sign in at all. Says my xbox cannot connect to xbox live. Connection test shows it getting on the internet just fine just cannot connect to xbox.

Tried. Connectivity works but cannot connect to XBox Live because of the update.