Although this is way later, I will add this response for others who may encounter this problem. My Kodak Easyshare camera also would not zoom, as it would shutdown when I tried to zoom. This occurred when the rechargeable batteries were completely charged, but I discovered that when I plugged the camera into a USB port, the camera zoom worked fine. I replaced the batteries with new non-rechargable AA batteries, the camera zoom again worked fine. In my case, the rechargeable batteries were at the end of their life and just did not have enough current to make the zoom function work, so the camera needs batteries which have sufficient charge, and rechargeable batteries must be adequately charged and they cannot be too old batteries for the zoom to work OK.
What is interesting is that if the rechargeable batteries are old but fully charged, most of the camera functions as normal, but the zoom will not work.