?? Charging lite NOT ON, is this the light on laptop, or on charger.
Generally 3 choices:
1) Charger (AC adaptor), can you try a differ charger.
... With battery removed, does AC Adaptor power on the laptop??
3 Laptop Input circuitry. ie the power jack, or the circuitry that converts the 19VDC from ac adaptor to the Lower voltage required for charging/operating the Laptop (ie +12VDC).
A digital Multimeter is needed in many cass. A DMM is cheap < $20 USD). Very simple to use, jst google "how to use a Digital Voltment".
Try removing the battery and operate the laptop only from AC. Does it work like that? If it does, your battery needs replacing. If it doesn't, then it's your charger (or plug) that needs to be checked. You can do that with a voltmeter. Or you can take it to a shop to check it for you.