My ipod 4th gen wont charge?

it's basically brand new I JUST bought it brand new not even a month ago and have no ida what happened, when I plug it into my computer nothing happens but when I pug it into my other ipod touch it charges. it cant bebeause of my computer or cord because it worksfor my other ipod and I've already held the lock and menu button down for 10-15 seconds andit still won't chare- which also mean i cant add more music. PLEASE HELP IM IM MISERY >.>