Originally Posted by toshik1
Yes the battery charges fine, I just don't see the green confirmation light.
If that's the case, then most likely the LED output (Pin #1) from the charger IC has died. The only remedy would be to replace the charger IC. No big deal if you can solder. The following ICs are compatible: SGM4054, SGM4055, TP4055, or AS4054. The 5 or 6-pin chip is located at the top edge between the battery power connector and the microphone on the side with the card holder, reset switch and USB socket. The pin in the middle, opposite pin #2 is not connected or may be missing. It depends on the model.
However, as long as the battery charges correctly, I wouldn't bother, The battery will be fully charged after max. 2.5 hours. I have a test camera which has been permanently connected to a power supply for many months and I can still record for ~35 minutes.
A word of warning
: I don't recommend leaving your camera permanently connected unless nothing bad can happen in case your battery explodes or catches fire. You should never charge LiPos unattended anyway.