Battery Drains ... always

upon where the battery came from it could be it, or a power drain from the computer. There's a lot of cheap batteries manufactured in China that fail right out of the box, or have charging "issues" (you should expect a free replacement from the vendor in such cases).

When running any computer there's often not a lot of excess power to charge batteries available so it's no surprise to me that it charges only when off since you seem to have something draining system.

Until you get the new logic board remove the battery when the unit is off but not charging.

FWIW updating or installing large applications while running on battery only is not good practice. In fact many Mac OS installers nag you about not being plugged into an external power source because a failure in the middle of an update or install could pooch your HDD.

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