If you aren't getting any magazines then you certainly should be able to demand your money back and cancel any future payments. You may want to complain to your state's attorney general office, they may well have a consumer complaints division. This response is for informational purposes only and is not offered as legal advice.
Assuming you have stated everything, you are the victim of fraud. If you have received nothing of value or not received what you were supposed to, you may rescind the contract by notifying the publisher at once. If you paid by credit card, you should notify the credit card people notto pasy the bill and why. Typically the vendor is paid immediately, but the credit card company will freeze the vendor's account in the sum of the contested amount until the matter is resolved. I would seek the help of a Consumer Affairs person in the District Attorney's office or ask your local police what to do if you have been defrauded. Fraud is a crime and also a civil wrong. Good luck.
This is not legal advice, but rather an answer to a hypothetical question from someone I do not know.