Why do I recieve the message "Your console cant connect to Xbox Live"?

You could have very well been banned but only if you did things that go against the Xbox Live Terms and Conditions. But I suggest checking your membership online to see if it is no longer activated or recover your account. I used to have this problem but I went to Network Settings, and tested my connection then after everything was all good, I could sign in no problem. If none of these work, I suggest calling Xbox's toll free number and 1-800-4myxbox. They always have someone there to help you.

recover your account

ugh...try connecting then? lol duhhh

here's a hint: "I" before "E" except after "C" (I could keep going, but I don't want to confuse you).

lol did you pay for it lately if yes try connecting it to a modem or router idk there always the call microsoft option it could rely help

do you have enough time or did you pay for xbox live?

your connection might be getting interuppted by something else or you have a bad connection.

try connecting to the internet.

Yes