My kodak easyshare M320 isn't charging with the USB cord and my camera won't turn on either because there's literally zero battery left.

Possible solutions:
Remember you need to turn the camera on when transferring.
Try a different USB outlet
Try a different cable
Try a different computer.

If all fails please contact KODAK in order to arrange a repair or order a new cable. Remember your USB cable is covered under the same warranty as your camera, so remember your serial number when calling:
http://www.kodak.com/eknec/PageQuerier.jhtml?pq-path=14563&pq-locale=en_US&_requestid=3490

I had this problem too, after about 3 minutes the charging light would go out, I found the problem appeared to be either my charger or the wall socket, for some reason now it is charging, try plugging it in to different sockets, and watch the light, after 10 minutes you can be sure it won't go out. After charging DO NOT use your camera for about an hour, I found that if you use it right after charging its a real pain to charge again, and it acts as though its battery is still dead.