Great American Reader Wont cancel because I passed the 3 days to cancel, but I didn't know I was signed up till 3 months later!! Internet

Im a college student who one morning got a call from some guy saying i won a 1000 shopping spree, immediately i said "no thank you" i didn't want to be rude, but he said this is not not a scam(i should've hung up) he said there was no purchase necessary. So i heard him out and agreed to receive the shopping spree. He tells me i will be receiving a call from his manager to see how he was with costumers. I said ok and went on with my day, about 30 minuets later i was in the dinning hall got the call, and spoke to the women and she immedietly started to talk to me about magazines and told me of the 49.90 deal i figured great, and never did she mention if i wanted to cancel i had 3 days to do so. I didnt get any magazines for 3 months. By the time i had realized i was getting charged for magazines i didnt get, my father was already trying to cancel the subscription because he gave me the card. 

 When my father told me that i had signed up for 5 years of magazines i was schocked. When i called to cancel they had told me that was not possible, when i asked why they never answered and said they just couldn't do so. Instead they said i could just pay it all at once and it looked appealing to me to just pay them like 300 bucks and it would all be over, but the man told me it would $8,000 and i was floored that they would think anyone would pay that much for magazines (ones they didnt want in the first place) in times like these. My father cancelled the credit card and they havent received payments. They started to call me and leave me voicemails that by the 2nd week of them calling 3 times a day i just erased. I dont know what to do because they keep sending me magazines, magazine i would never order like Parenting (im a freshman in college why would i want parenting magazines). I dont know what to dont pay i will ruin my credit or that they'll take me to court.

What i dont understand is why they wont cancel if the magazine companies are so willing to cancel, and even give you a refund if need be. Any suggestions on how to handle this would be greatly appreciated!!