Am i still responsible for a contract if i did not submit? Meaning they do not have my signature in agreement.

I paid a down payment of $500 (non-refundable) over the phone for a banquet room. When I went to see the room, I hated it and cancelled. Leaving with the contract in hand. Months later, exactly 13 days before the wedding they called us to start planning. We told them we cancelled in person. They said we violated the contract and owe the half of the entire cost. Help? We did not submit the contract. Do we still owe?