Chosen Solution

The magsafe connector stays lit up in green, and I assume my battery is dead, because I haven’t used this machine for a while. I googled. I tried the control-option-start button trick, no love. I opened the machine, disconnected the battery, waited a while, reconnected and tried again to no avail. Not long ago, I checked the battery condition and it was good. So, no charge getting to it I think. Could this be the magsafe card, or the DC? Any and all suggestions/diagnostic tips appreciated.

By chance did you have a liquid spill at some point? This sounds like liquid damage. Your logic board is the likely suspect here. Within it is the power control logic which switches the MagSafe power to either the battery charge or running the system or both! Something in this logic or deeper in the CPU logic has a problem.