My wow account is banned with no reason

OK, I don’t have all of the facts that I need to give you a well-informed answer here Showtimebre, but I will cover the most likely scenario.

As you cannot login to your account, we will assume that the email you are speaking of here is genuine. If you have not done what the email says you have done, then it means that somebody else has. Unfortunately, this is an indication of having your account compromised by a third party. If the email is indeed legitimate, it should have full and clear instructions on what you need to do next, but to help you out here is a link to our very useful sticky on the matter;

►► Account Hacked/Stolen? CLICK HERE! ◄◄
http://forums.wow-europe.com/thread.html?topicId=12304393621&sid=1

I will highlight the part that applies to your potential situation;

Q u o t e:

• I’ve received an email from Blizzard telling me that I’ve been banned for ‘involvement in online-trading’ and/or ‘use of 3rd party software’! Why?
  
  
  Compromised accounts are, unfortunately, often used by those responsible for exploitation, such as advertising or ‘farming’ for gold. These mails and the subsequent suspension are part of our preventative measures, and prevent further damage to your account. The only way to gain access again is to speak to us first, something you will likely need to do anyway.
  
  Rest assured that you will not be held responsible in these situations, and we will completely remove any warnings/suspensions once your ownership of the account and the circumstances have been verified.

You then need to follow the steps outlined in post number 3 (entitled ‘Unable to Login’).

We will take it from there and do our very best to help you out every step of the way.

Good luck.

This is also covered in that very same sticky Showtimebre;

Q u o t e:

• I get asked for an authenticator code when I try to login, what’s going on?
  
  
  This happens when the person responsible for the theft of the account uses a Battle.net Authenticator in an attempt to make it more difficult for us to assist you.
  
  The truth, however, is that our ability to recover your account and reimbursement lost items is completely unaffected, and the necessary steps remain relatively unchanged.
  
  Should you find yourself in this situation, please follow the steps outlined in the Unable to Login (http://forums.wow-europe.com/thread.html?topicId=12304393621&sid=1#3) section below so that we can remove the authenticator for you.

Best of luck.