ebay is a strange monster, and unfortunately i've had experience with their 'sellers protection' before, so i'll walk you through some tips:
1) check the payment notification from PayPal when he paid you. it will say in it something like this: "Seller Protection - Partially Eligible (Item Not Received Only)" that is what determines your protection for that particular purchase. your protection differs depending on the particulars of that transaction. sometimes, you have none at all. others, there is little the buyer can do if something is legitimately wrong. if you got delivery confirmation or something, just go to your paypal, add the delivery confirmation number to the transaction, and tell him to fuck off, because its not your problem. i mean, if it is for item not received only, and not something else. if paypal can go to the usps website and track the package and see he got it, that's all they need. the buyer can whine all he wants.
if it doesn't say that in particular, or even if it does, you can see paypal's policy by going to that particular transaction and there should be a link from there.
2) ok, let's say he does elevate it to a claim. paypal will ask you for a couple things, namely ID, any tracking/delivery numbers, etc... if you listed the listing "as-is" or ANYTHING similar, thats a great thing. *if* you said the screen was in perfect working order, there may be an issue unless you had dated pics in the auction itself, showing the screen. DATED pics, mind you... *if* you provide good info, especially the delivery confirmation/tracking numbers, paypal will be sympathetic towards you. remember, they made their money from you being paid through them, they didn't charge this other dude the fee... they want sellers to be happy, for the most part.
3) first off, however, he would need to open a dispute, then after that he's still got to file a claim which basically means PayPal decides who is right. and, if they don't judge in your favor, you'll be charged through whatever account you have on file with them. But, they suggest dialogue with the buyer first, before the claim is raised to their arbitration. wait, reverse the words dispute and claim. my vocabulary is backwards, but logic still the same...
if you get negative feedback for this after the dispute or whatever, you can appeal it with ebay, if its obviously a retributive act. their policy keeps changing with this stuff though, not sure what it is now.
i think the only way you are going to be in trouble is if you sold it explicitly with the screen working 100%, and/or it never arrived. his absence in alerting you to the issue immediately indicates he was either aware of the screen problem (and has since found it unacceptable), he didn't open the package until now (which his language indicates otherwise), or he is trying to pull a fast one on you and the problem just started (not your problem).
good luck (: paypal won't let him keep it and get it free. don't worry about that. you'd have to have it returned (you'd prolly get stuck with the shipping bill) and then upon proof of receipt he'd get the refund. the only way this wouldn't be the case is if it never arrived to him, then they do offer refunds without return of merchandise.
