?? 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".