Hi, it sounds like there’s definitely a power problem between the battery and the motherboard. If the light turns green immediately when you plug it in, that means it’s not detecting a battery to charge. Does your computer recognize the calculator at all when you plug it in? Are all three battery contacts (in the battery compartment) clean and undamaged?
What were you doing with your calculator right before it stopped working? Have you dropped it or accidentally spilled anything on it?
I’m not really holding out hope, but there’s a chance TI-84 Plus CE Recovery Techniques. may help.