Removed it. Seems to work now. So either the battery was the problem, or it just magically decided to work now. Honestly, wouldn't be the first time. As I have a couple of Apple II PSUs that gave me nothing but problems for years. Clicking, ticking, no voltage... Then one day, they just decided to work, and have been reliable ever since. I swear, I didn't do anything to them! I hate it when that happens. You never know if or when it's going to fail. And as long as it's working, there's no way to trace the potential fault.
Also, I tested the Hard Card. And... It's dead. No big loss.
In any case, I think I've taken this thing as far as I can until the replacement pads arrive for the keyboard.