Hi Charline, I can think of a few things it could be. The first thing I would suggest doing is an SMC reset, instructions from the Apple Website below. If the battery is nonremovable Shut down the Mac. Plug in the MagSafe or USB-C power adapter to a power source and to your Mac. Using the built-in keyboard, press Shift-Control-Option on the left side of the keyboard, then press the power button at the same time. Release all keys, then press the power button again to turn on your Mac Second thing I can think of would be to replace the MagSafe connector on your logic board, however, I have a feeling with this model the MagSafe is part of the logic board and that would be a very expensive replacement Good luck
Hi John If you plug in an external monitor do you get anything on that? It could be one of two things, an screen issue or a logic board issue. If you haven't already, do a PRAM reset and see if that makes a difference. Hope this helps and good luck!
I think it's pretty safe to say that the battery should probably be replaced. We have had this issue a few times in the department that I work in and a battery replacement was the required fix. I'm guessing you have tried an SMC reset?