Exit Easyshare and start Windows Explorer and look for the camera as an extra removable drive.
If this doesn't work, buy a card reader (presumably the Kodak uses SD cards) for a few bucks and plug that into the USB socket of your computer.
I just bought the same camera, and I'm having the exact same problem. And, I also tried plugging the card reader into the USB port, and it doesn't work either. Any other suggestions? This is very frustrating. :-)