I dunno, but it seems to me that even with a non-functional battery, your MBP should work while plugged in.

I can only guess, but the green light may mean that the battery is fully charged as respects its ability to take a charge, i.e., 0% = 100%?

The new Great Equalizer is the SEND button.

In Memory of Harv: Those who can make you believe absurdities can make you commit atrocities. ~Voltaire