Could be a problem with the cable, your USB port or any software the Kodak relies on to transfer pix.
The simplest solution is to get a card reader and access your photos that way.
If you have a desktop computer it is possible to add a PCI card which carries USB sockets. If you have a laptop and your's has a PCMCIA slot you can buy a PCMCIA card which carries USB sockets.
Test your USB port with a device other than the camera -- if necessary borrow a USB flash drive (aka memory stick) from a friend or buy one for a few dollars -- they are always useful.