You could keep it, as a spare battery, spare SD card, for your next Kobo.
If you were so inclined you could use it as a devboard (like a raspberry pi), who cares that the screen doesn't work, it still has wifi and stuff, a fully functional Linux platform
Selling it on Ebay might bring a few $$$, see it as a small discount for your next device, who knows.
I could use a broken Kobo Glo/Aura for testing purposes, got a Touch from Ebay, but for some reason the newer Kobos (Glo, etc.) get "high" bids even for completely broken devices. Not sure what people do with them (well, the above, but how many people would want one for that instead of buying an actual raspi?)
If you are very very very lucky you could also find a replacement screen on Ebay. If someone has a bricked reader and for some reason decides to sell rather than un-brick it. Some people might not know about un-bricking... if they can't Google...
It's a dangerous/expensive experiment though, sometimes screens look fine even though they are really broken in reality. This one here is definitely broken (
http://www.ebay.de/itm/Kobo-eReader-...-/231651575343 ). Also some sellers are careless, the defective Kobo I bought from Ebay was shipped in a simple unpadded envelope even though I paid for proper shipping. It's already defective, right, what could possibly damage it any further? *facepalm*