macbook pro battery won't charge - indicator light fades out

My macbook pro will not turn on. When I press the button to check the battery charge level, I get no lights at all, and I hadn't used it for few days prior to having this issue, which led me to assume my battery was dead. I don't believe my charging cord is the issue because it works correctly when plugged into a friend's macbook pro. When plugged into my laptop, the indicator light on the cord comes on initially, but after a minute or so, it begins to fade out and then shuts off. I have been switching back and forth between my charger and a friend's charger every time the light goes out, and each time I swap the chargers, the light comes on initially and then fades out the same way. At first, I got an amber light each time I attached a charger. After maybe an hour of swapping, I am now getting a green light, indicating a full charge. However, I still get no indicator lights for the charge level. I wish I could remove the battery and see if the laptop will turn on, but the battery is not accessible on the model I have (A1278). Does anyone know what this issue means? Could it be resolved by just replacing the battery?