Magazine Direct Subscribed me to magazine order with OUT my permission and attempted to charge me Nationwide

I have no idea how they got my info but they have my name, number, address and a credit card on file.  luckily that credit card was lost and i cancelled before they can charge it.  They still call me once and a while asking me if i want to renew my subscription.  I recieved magazines for a while and had NO number to call or website or even the name of the company because everytime i attempted to cancel they immediately hung up on me.  I recently recieved another call and discovered their name and found them on here.  They claim i had a 5 year subscritption thats ending soon and ask me to renew and for a new credit card however I dont want to give them one.

at this point they've been sending me magazines but i have NOT made ANY payments and i am completely unable to cancel the magazines without providing a valid credit card.  Im hoping they dont have something that ties me to the subscription and end up charging me 500+ dollars. 

Any suggestins on what i should do??  anyting helps thank you