Do I need a new cable?

I just got a new iPod touch 5th generation and it won't charge if the cable is plugged all the way into my computer. I have to play around with its postition, reset it countless times, and restart my computer a few times for it to start to charge. Also, it charges for about 5 minutes, then disconnects itself. It also isn't showing up in my iTunes. Do I just need a new charger cable or is there something else I should be doing?