I don't want to pay for a broken chair
Why would you pay for something that is broken anyways?
I'm unhappy that the customer service was not honest with me and they are not refunding me for something that came broken.
That's not right that you have to eat the cost of something that came in as defective. Why don't you try and refute the charges directly with the bank. Usually they will get the money back for you.
I'm going to need a refund ASAP.
I think that you are correct and that they should issue you the refund. There is no reason for you to pay for a product that had came broken.