Broken USB port on iPod Touch

Recently when I've tried to charge my iPod Touch 3G, it wouldn't charge with my wall charger. If I moved around the end of the USB cable near the iPod, I would see it connect for half a second and stop. I've tried connecting it to my computer and it still wouldn't work. So I purchased a new USB cable/wall charger thinking the cable was the problem. However it still wouldn't connect/work. I've tried the same wire with my old iPod Touch 1G which worked perfectly but still wouldn't work on my iPod Touch 3G. I think the problem is with the port from inside the iPod Touch. Right now the battery completely dead but before it DID die it wouldn't connect. So the problem is with the port, not the iPod, not the battery and not the USB cable. Can it be repaired? I have an appointment with Apple this thursday. My iPod Touch 3G is still under warranty AND covered by the Apple Care Protection plan (or whatever it is called). Will they repair it? I know they can replace it with a brand new one, but I just want it repaired.