How can I obtain a $400 refund from PayPal for an item that never arrived?

The amount should not be an issue in question. If you are able to show that no such shipment was made, or you never received or signed for it - you have a case. Likewise, be aware, the Seller would just need to show a tracking number, etc. of the goods being shipped out to you. If that is the case, it would his/her word against yours and then the account history of both your accounts would be looked at to see, who is more habitual in returns and reversals.