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A green light would suggest the camera is switched on, and in essence the power from the AC power supply is powering the camera (not the battery). Might be worth double checking the battery is correctly installed and camera turned off, the light should go off or turn orange within a minute of plugging the unit on charge when the camera is off and battery fully inserted.
Do let me know if you need anything clarified.
Glad to hear you are now working and have got the camera charging, have a great day.