The primary problem is figuring out whether the charges are legal or not. You might have a continuing contractual obligation so you need to pay an early termination fee; or maybe not. (There is also the question of whether you think you don't and they think you do). The alleged obligation might be something one-time (i.e. an amount still unpaid). Whatever it is, they will not discuss it with you unless you have the security code, or you appear in an office with suitable ID. This non-discussion extends to requests to cancel an account.
The two things that you would need to do, in a letter (if a trip to the store is not practical), is prove that you are who you say you are, and to make an official demand to cancel the account (which you know was delivered, because you sent the letter certified. You may hire an attorney to handle this, or you can try it yourself first and get a lawyer if that fails.
There is no law that requires a company to discuss details of an account with an unverified person, indeed if they don't verify that you are the relevant person, you might sue them for negligently putting you at risk. But there is no law that lets them say "if you don't have the security code, we've got you for life".