I have a kodak c610 camera with the c613 dock but it will no longer charge when i put it on the docking station.

If I'm not mistaken only KODAK rechargeble batteries are suitable for this docking station. Please follow the link to the recommended batteries:

http://www.kodak.com/global/en/service/batteries/batteryDigCamChart.jhtml?camera=DX4900

Are your cam batt the recommended KODAK batt?
The dock will only charge the recommended batt.

Kodak sells three different package versions of their cameras. You can purchase one of their cameras with an adapter but no dock, with adapter and dock, or with adapter and printer dock. The dock and printer dock are also available on line (try eBay) as accessories. The dock is an extremely handy accessory, allowing automatic charging and computer connection. The printer dock though, at least in my experience, is a cumbersome and unreliable method of obtaining low-quality photos.

What batteries you use?

The camera docks only charge the kodak battery pack KAA2HR (you can buy this pack at the kodak website) or Kodak Li-Ionen batteries but they don't work in Your camera. So buy a battery pack KAA2HR from kodak and the dock will charge it ;-)

get a charger for the rechargable batteries. Charge the batteries and then put them into the camera. You cant really chare the camera..

Hi, I think I can answer your question, i just tried something with my camera and camera dock.

My camera came with a Kodak battery pack(pack that looks like 2 batteries connected together). When I place my camera with this battery pack in it on the dock, a green light comes on on the dock and the batteries begin to charge. However, when i place any other rechargeable batteries in the camera on the dock, it has no effect, my theory is that it must be a battery pack, possibly by the same manufacturer so that it will charge correctly

First, the dock will charge only the batteries that came with the device; not other rechargeable batteries.
Be sure that the Kodak battery is inserted correctly, the door is closed securely, and that the camera is securely seated in the dock with the power cord secure to both the dock and the AC outlet. The USB cord does not supply power to the dock.
Hope this helps.
DigiChick

camera should have had a usb cable in package-simply plug cable into camera and usb port and computer should recognize and offer to start transfer-if not use a memory card reader to download pics also works great and doesn't waste batterys on camera while you download

Not sure if this will help, but you might try removing the batteries from camera, then see if it responds on the dock, if so it is most likely bad battery. That battery should be easy enough to find at locally. You might wanna try the Interactive Troubleshooter on Kodak's site. http://www.kodak.com/global/en/service/products/ekn030483.jhtml?pq-path=6861

Camera or battery dead.