I'm a teenager who started fixing ipods when I was 12. I buy them on craigslist, fix them, and resell them. I hope I can provide help from knowledge of my many repairs, and also ask some unique and new questions!
Could be a problem with the battery. I know it usually doesn't work, but try the 5 R's: http://www.apple.com/support/ipod/five_r... If that doesn't fix it, bring it into your local apple store. It is still under warranty because it is under a year old, and they can replace it for you.
The iPod classic is extremely difficult to open, but it is possible to be done. Here is the link to the repair on iFixit: iPod Classic Headphone Jack & Hold Switch Replacement You have to buy the correct part, either a thin or thick, depending on your model. Good luck!