You've been banned by an admin or mod. You can't login to your old account. I wouldn't always recommend this but if I was banned I would do this;
So, I would forget about the other account a create a new account. I will pretend that I am a totally different person from the other account and not ask to un-ban my old account. So I would go on with this account, help users and do that stuff and once I would receive enough trust from the staff, I would confess I was this person and tell them I only did it so I could continue enjoying this game and basically start fresh! I'm sure the staff will understand you and maybe one day un-ban you. Don't count on it though. Thanks for reading! Comment below on what you would do or your thoughts!

Lol cool i'm a good person but for people who have been banned and really DO care about their accounts could really try that.

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Good this helps. But I cant make a new penguin. It just says Im banned. I made a small mistake, my friends penguin was blamed for it. Now im demoted and banned

This may help many of those who have made many of mistakes in their past experience in Old CP. If they create a new account, you will have absoutely NO clue that they are that person, unless they give you clues that lead to it being themself. It is a great idea that many will use to make a fresh start and do the right thing and make good decisions. I like it, as long as people don't take too much advantage of it, which we know is not going to happen.

What if he was IP Banned?

Cant really do that when you are banned from the website forever for no apparent reason.