What weirds me out about this is that the charge LED just shows as fully charged when I connect it…
Is it trickle charging at that point, do I plug it in and leave it?
Could be as simple as a bad spot weld on the battery. When the charging circuits floating, it might see the input voltage on its output and no current and interpret it as a fully charged battery. Could also be a damage of the protection circuit or even an internal damage in the battery.
Don't try to charge it. Something is wrong with the battery and you don't want to burn down your home.