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TL;DR, I got a dodgy battery that doesn’t like to charge, so the battery is disconnected right now and I’m using the laptop in AC-only. What happens if I try to plug the battery in while the Mac is powered-on and running?
I would’t try that if you have a dodgy battery! You could damage the logic board charging logic. How about we figure what’s happening. Let’s first disconnect the battery as well as the MagSafe charger (any anything else thats plugged in the ports). Now press and hold the power button for 15 sec so we fully discharge the logic board. Now carefully plug in your battery and then the MagSafe charger. You’ll want to have already setup a ISB drive which you’ve already downloaded CoconutBattery as you’ll want to install it to your system and take a snapshot of the apps main window and post it here for us to see Adding images to an existing question