How should i deal with my aol broadband dispute?

I moved from Aol broadband to another provider 29th september 2009 as I wasnt happy with the service they provided to me they have twice in 1 month blocked my home phone and turned my broadband off due to there mistake .AOL continue to contact me by telephone saying I owe them money as I have a contract with them till february 2010 they want the money for the time my braodband was blocked which was over a month and untill february 2010 . I asked them to send me the contract with my signature on but they said they didnt need a signed signature the contract they had is valid without a signature could somone tell me if this is true or not and what I should do next thanks GEOFF