Battery not charging after changing battery and MagSafe

Changed battery a while back and it would not charge. Changed mag safe twice. Got wrong one the first time. LED never goes amber always green. MAC will work unless it’s running something demanding any kind of additional power. Laptop will then shut down. Not sure if I got a bad battery. Is it possible for my power adapter to power the computer, but somehow not charge the battery?

Is there anyway to test power adapter? Can I troubleshoot this to logic board? Should I get a new battery in case the one I received was bad out of box? Or do I just keep shotgunning the troubleshooting?