Hi Benjamin,
You have to return your broken ipod before Apple will issue a new one, because it may be repairable.
If it is any consolation, I have to give Apple some really good credit here. I am in the UK and my ipod mini went dead - tried everything, no luck.
I then filled in the
repair service form online, (You can change country at the bottom if necessary) and within two days a delivery guy came to my door to hand me the packaging that I had to send my broken ipod back in. He also waited while I packaged it so that he did not have to make a return journey to pick it back up.
By day 3 it had reached Apple, by day six, I had a brand new ipod delivered to my door that I signed for. All in all it took Apple six days, (and a weekend was included in that,) and it didn't cost me a penny, nor did I have to leave the house.
First class service. The only other company to have offered a better service is Proview. Both times when my TFT monitor became faulty, less than 24 hours later (the very next day infact) Proview delivered a brand new one to my door, taking the old one back with them - twice this happened.
I doubt I will ever get service like that anywhere else, but Apple comes a very close second!