Kodak ls 753 recharging problem

I have a kodak LS 753 FOR two years now and today when I tried recharging the battery the green light lit up after sometime indicating full charge . However the camera didnt turn on . This is the original battery that came with the camera and I have used it extremely less ( not clicked more than 200 pics in the last two years ) .
How long does the battery last (its complete life before replacement ? ) and how do I conclude that its the battery thats faulty and not the charger . I last took pics for this camera today morning before recharging and they came out well . Please help . also suggest the best place to buy battery for LS 753 KODAK incase u think the battery's life is over . thanks