Ruling out a faulty battery for strange issues

I had recently picked up a second hand 3ds a couple of days ago, which was all in working shape (save for a faulty SD card slot). However I had noticed that while it has no problem turning on, the system will make a 'pop' sound and completely turn off when the power button is pressed (while the system is on), instead of going to the "In Sleep Mode You Can..." screen. Further experimentation showed that while the battery would charge, turning the system on while plugged in would cause the boot to abruptly stop (with no sound made), and the charge indicator to suddenly turn off.

I figured it would be worth trying to swap the battery, as the system went from having two bars to flashing red in about 10-15 minutes. I haven't had any of these issues with the new battery, but I'm still questioning whether or not it was the cause of the issues. I don't like tossing out components if I have doubt that they're broken, but I don't want to keep a potentially defective battery in my possession.