You need to confirm a few things, and these are the FIRST things you need to do -

The NJ address - was this a shipping company that forwards parcels overseas?

The signature - in NJ, I assume. Was this an agent for the buyer, or an agent for the shipper?

Did it go overseas? If it did, you are NOT responsible for the final condition, nor is UPS. Your responsibility, as did UPS's, ended at the shipping address in NJ. Anything beyond that is the responsibility of the shipper.

Domestically, UPS sOcks and you will not win. You have better chances winning the Mega-Million lottery. PayPal has a tendency to believe the buyer over the seller. In both cases, though, it should be noted that the complaint was issued a MONTH after it was 'signed' for. UPS and PayPal will most likely deny payment or coverage, and really, there is no need for you to cover it. For all you know, it could have arrived safely (assuming a true domestic delivery, but doubtful) and the new owners had a party with drunk revelers and the speakers were damaged there. Or on stage, when the lead guitar member smashed his guitar over the speakers. You just don't know.