1) the laptop doesn't power on without a battery
2) the light which would indicate that the laptop is plugged into the ac adapter is on when the ac adapter is plugged in.
3) the battery charge light is also on.
The battery does not charge but instead depletes while it reflects charging
The AC adapter is fine, tested with other laptop.
The battery is also new and works fine on other laptops
When you tested the charger cord on other laptops did it both power the laptop and charge the battery? Also, on your own laptop, did you try powering down the device and then seeing if the battery will charge?
I ask these because when a cord is going bad it can make it only able to do one thing at a time. This would lead to the battery not being charged when the device is on and plugged in. It can also be why it is still draining.
Another option is that there is a form of malware, virus, etc. software on the device and it is the cause. You may wish to check that as well.