If you have proof that something was broken when you moved in, such as the drawer, make a copy and send it to the management.

Did you do a walk-through with someone before you left the apartment? Did you take pictures of how things looked?

I'm sorry to say that if you can't prove the damage was in the apartment before you moved in, you may have to pay the bill. I'd try contesting the things that you are sure of, like the drawer, and paying for the damage that you know you caused, like the wine on the carpet, right away. You may get lucky and they may reduce the bill.