Chosen Solution
My Macbook Air only turns on when I disconnect and reconnect the battery, and connect the charger. After turning my Macbook on, I can use my laptop without the charger.
Try an SMC Reset SMC RESET Shut down the computer. Plug in the MagSafe power adapter to a power source, connecting it to the Mac if its not already connected. On the built-in keyboard, press the (left side) Shift-Control-Option keys and the power button at the same time. Release all the keys and the power button at the same time.
Doesn’t work, many times on new battery, it’s green charging, if I unplugged the cable the computer dies, it’s a new battery… a Duracell and the second battery I had from them with the same problems after a month of use.