If you put a fully charged battery on the shelf for a few days to a week, and then put it in the camera, is it still fully charged, or has it already noticeably discharged? This will help determine if it is the camera or the battery. If the batteries are self-discharging outside the camera, they are worn out. LiOn batteries can only be recharged so many times and typically need to be replaced every 18-36 months depending on the usage patterns.
If they are only discharging while sitting in a camera that is turned off, odds are you have a short somewhere in the camera. And it isn't doing your batteries any favors either by deeply discharging them.
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