Can I get my Ipod Touch 4g Fixed/Replaced?

Ok so for some reason my ipod wont charge or connect to anything-It stays at the low battery screen(With the lightening bolt underneath it). It won't do anything. At first I thought it was water damage, but the square or circle thing in the headphone jack isn't red, it's white. It's just refusing to work. Can I bring it into the Apple Store and get it fixed for free? I'm still under their one year warranty.