Why doesn't my MacBook Pro battery charge when the computer is on?

I bought a replacement battery for my trusty MacBook Pro. I am frustrated because it charges for a few minutes with magsafe light on, then stops charging. Even if I unplug the power cord & try again, the same thing happens. It only consistently charges if the laptop is powered off. If you can't charge the battery while working on the computer, then what's the point?

If anyone has tips or advice, please let me know.