They won't accept a receipt from eBay, as eBay's not a licensed reseller, and they consider the new, in box item "second hand."
TBF, this should be a given. Assume anything you buy on ebay has no warranty, even if new-in-box. They should still fix it, imo, given it's a known problem but I'm not surprised by them not accepting their receipt and trying to save money where they can.
ungrokable's advice is probably your best option.
I recently did it anyways, we'll see how it works out lol. Going back to school to change careers.