Apple Ipod Nano

I bought my son an Ipod Nano from Apple for his birthday 3 months ago and it has already broken. The screen has 'gone out.' It comes up as black and you can't work any of the controls.

Apple will not stand behind it even tho it has a warranty. They say it's not covered under the 'limited warranty.' We even spent money on a protective case for it to protect it and he has always carried it in that. They also say they won't even fix it if we pay for it! So basically I've spent $300 on the Ipod plus accessories and now we get to throw it in the garbage can?

Anyone here had a similar experience?

Gwen