dispute with broker/landlord

[jqgatsby]

Around february 8th I found, through a broker, an apartment in downtown manhattan. At the broker, I signed a lease and other documents (not sure about everything signed because I wasn't given copies of anything). They wanted me to pay first, security and one month's broker's fee before february 15th, the move in date. I was getting my bonus on february 15th, and wouldn't have the money until then. I told them I could pay $800 now. They debited my card $800, and sent a check to the landlord for the first and security. I wrote them a check for 3 months - $800, which they would cash on february 15th, when they would give me the keys. I think the check was made out to the broker. Over the next few days, my sister, who had been planning to move in with me, decided that she didn't want to. I called the broker and said that I wasn't going to move in, and cancelled the check I had made out to them. They told me it was too late, the landlord had already been sent the signed lease. I called the landlord and told him I wanted out, and the landlord said that if the broker could find someone else by March 1st, then that person could pay the broker the 2 months (+ whatever fee), take over the lease, and it would be fine. I called the broker and told them this plan, and she assured me that they would be able to find someone by March 1st, since the rent had been reduced. They would keep the money I had already given them. I thought this settled the matter, and went on with my business, eventually renting an apartment of my own. Around March 15th, the broker called me and said that in fact they hadn't rented the apartment, and the landlord had just cashed the checks from them. The broker wanted me to pay them the two months rent, for an apartment that I never lived in or received keys for. Do I have to pay them?