Go to the Apple/ipod website. They give you ideas for troubleshooting. Sometimes it's something as simple as just re-setting it.
My son's mini broke just before Christmas. He had it one month. It was running, but no sound was coming through the headphones. We tried different headphones, and it still didn't work, so we knew it wasn't that.
I went to the website, read through it, and filled out a form for repair. They immediately sent us a box with label, and we called DSL to pick it up per their instructions. The next day we got an email from Apple saying that they received the ipod. It took a couple of days, and they sent us another email saying that a new mini was on it's way. Again, the next day it was at our door.
It cost us absolutely nothing. Not even shipping! I'm really impressed with Apple. My husband was in disbelief. He thought there was no way they'd just give us a new one.
Be careful about putting it in your pocket or in a backpack. They are sensitive.