You can see date of purchase on ebay or in your paypal's transaction history (or check your visa card's transaction histories if possible). I don't think you'll save something valuable from them, maybe it's better to sell on ebay. Now I checked prices on ebay and seems it's average 200$ for broken gtx1080. It's so pity to lost such a great card, btw I never buy from ebay, always check prices on nowinstock and get some good catchs when I am very lucky.
there was a buying frenzy, i was not aware that nvidia itself will dishonor its warranty, evga and asus did great stuff on replacement, i am not sure whether nvidia will honor ebay purchase receipt, the best i can do is to inquire the seller because i have kept the detailed log of the purchase: seller account and serial No. etc. But if the seller is a volume seller business type, chances are they will not even bother giving the purchase date and receipt so probably i get stuck with those.
I may try to list on ebay at fair price stating it is defective and take your chance type of sale.