Check for CORROSION INSIDE THE TERMINAL that fits on the warning light connector,
Connect a voltmetre to battery run the engine WITHOUT THE lgnition warning light wire connected, touch a LIVE onto the terminal on alternator on which warning light wire goes, it should now start charging, if it does not it is duff.
When you say there is no warning light(charge), this should give you a clue, if it was not working the alternator would not start the charging process at all ever as it needs a LIVE FEED THROUGH BULB ALL THE WAY DOWN BLUE WIRE to ENERGISE FILED WINDINGS IN ALTERNATOR, to initiate charge process, once charging process initiated it outputs POSITIVE at this terminal and light goes out as two positives do not make a bulb work(warning light).
The bulb for charge warning may just have gone black.
tabetha