Will they fix this broken itouch?

If you have accidental damage warranty Best Buy will repair it for free. If you don't, it will cost just over $60 to replace. Best Buy has the Geek Squad that repairs iPods, but they may sub it out to Apple. If the iPod goes to Apple, it be placed with a all the other iPods and and be repaired and you will get one of them. There is not guarantee you will get your some iPod back and it will come to you as if it were brand new. Meaning nothing you added will be on it. It the Geek Squad can repair it, you will need to ask them first. In all cases Back up your data. If you have your iPod repaired by a third party. Something like that would not be noticeable to Apple and your warranty would not be affected as long as you don't tell them. Don't worry...Worst case $60.