Chosen Solution

I replaced the battery in my 2010 UNibody 15" Macbook pro. The replacement battery has fully charged, but the computer won’t fun off of the battery. When it’s plugged in, the batter indicator lights as well as apps like Battery Monitor show a full charge and perfect battery health. However, as soon as I unplug the power cable, the computer shuts down, just as if i didn’t have a battery in the machine.I’ve tried both an SMC reset as well as a PRAM reset. No joy - any suggestions?

Sadly, your systems power logic on the main logic board is having problems switching between the two power sources. One of the MOSFETs has failed and will need to be replaced. This often happens in this series. Time to find someone with good micro soldering skills to fix your logic board.