The room wasn't as showed and I moved out

Hello, I am in new york for 3 months, I found a room to rent online while I was in london. I was sent a video with the room and I was told that it will be cleaned before my arrival (same as the kitchen and bathroom). I paid in advance January and gave a deposit. I have to move in 16 days later in january and the apartment wasn't clean and there was damp that I wasn't showed on the video. the mattress was unfit for use, the bathroom and the kitchen were dirty. the bathroom door and the storage door were broken. I was sent a lease but I never signed it, I was told that we will sign it when I arrive. 2 days after my arrival, I asked to move out and I asked for a refund of at least my deposit but the landlord don't want to pay me back. Is it any way I can get my deposit back? Tanya