Absolutely no reason for you to pay for an item that was damaged by either the USPS or bad packaging. Now the USPS has apologized and the pic you showed clearly showed signs of trauma. Some here are defending the USPS to the hilt, and that is their right. I say, they damaged your property, period. They broke your item. You paid them to bring it to you, and they broke it. It is really that simple.
Your vendor, however, may be the easiest source of recovery for you. If you paid with PayPal you have 45 days to dispute it, you will get your money back. Credit card times vary by vendor, but most have similar methods. If you get your money back, the vendor will collect from the hammer-handed drones at the USPS who have repaid your trust in giving them delivery business with stonewalling, attitude, and obfuscation. It is too bad, but if you do nothing, you will be the one who paid two parties for a product and received nothing. What is fair about that?
Now they (the USPS) admit they have done you wrong, but will not remedy it. A complete disgrace, and no professional organization would behave the way they have in this case. There should be no question. There would be no question if UPS or FedEx had done this. They would just make it right.
You will no doubt next time order shipping for critical items from someone who is accountable.
EDIT: I see you had money taken from some account, so the credit card and PayPal avenues are closed. Like worthatry suggested, talk to the Bank. In the future, always use PayPal if you can. It would have protected you in this case.