It really depends, and 2 months is usually a very long time for credit card companies to issue a refund. The thing is you bought from a guy on eBay -- not a Nokia store.

If you can, contact the eBayer, and ask him to provide you with his proof of purchase (assuming it's an individual). If it's a retail store, ask them for their bulk purchase agreement (or something like that, the name changes from country to country). Basically, the store's proof of purchase.

Either way, the item came from Nokia. If you're lucky, it's an individual who still has the receipts and you're within one year of the original purchase. If you're unlucky, the warranty is expired or it's a store and they can't help you.

Either way, if the eBay ad said it included full warranty you should challenge the sale through eBay directly (PayPal and eBay are very much integrated, so this is very easy to do).

Regarding asking refund from your CC company, like I said in the beginning, because it's been so long it's going to be difficult (unless you have Premier services in which case you in some cases get up to 180 days from DoP). You can try, but I think you won't have that much luck.

Repair usually doesn't cost very much. If you get a good contractor it can be done for under $100 (don't forget you have a device which is a few years old, warranty only goes for that long).

Yes, they told you that they would definitely cover it, but they probably assumed that you bought it from a Nokia seller or something (they don't really think out of the box -- the processes simply aren't in place for such scenarios, ironically). Last thing you could try, go to a Nokia official reseller where they still sell N810s, and give one of the sales guys a $50 so he gives you a proof of purchase, then submit the device again with the "valid" PoP.

There's a lot of ways you can "beat the system", but it usually involves shelling out. Sorry to hear this happened to you. Good luck though.

PS: I once had an N810's screen fail on me. Because my warranty had expired some time ago, and I bought it through some guy on eBay in the US, I knew I'd had to pay. I bought some screwdrivers, took the device apart using the repair manuals (widely available on the internet, swing by IRC if you need help finding them -- watch out for viruses) and reconnected the connector myself. All good to go.