You bought WoW and Burning Crusade your WoW got banned but can you still install Burning Crusade and play on that

If your WoW account got banned and it is permanent then you will need to buy a completely new account from a retailer like walmart or bestbuy and if you wish to have The Burning Crusade enabled on the account you will have to upgrade it which can be done online now I beleive. But you will need to upgrade the account again.
In addition: you also have to purchase a new burning crusade key