DS Old and dead?

Honestly, I'm not entirely sure. Mine was basically perfect when I bought it, so I never had to contact them myself. I'd guess it's anywhere between a week to two weeks, though. If you decide to contact them, they'll tell you how long it's going to take (which won't be too bad) and then they'll ask you if you'd rather wait a week or so to determine whether or not you want to send the unit in.

The thing I'm not sure about is whether they give you a brand new unit or if they just replace the screen. If they ship you a brand new unit, I can't imagine it taking much longer than a week. If they change out the screen, I know that they send out "loaner" units to the customer while their own unit is being repaired. My confusion is to whether or not they actually repair units with dead pixels and return them, or if they just replace the entire unit.

Like I said, your best bet is to email or call them.