MacBook shows no signs of life

Are you getting any response when you press the battery checker button on the side, do any of the LEDs light at all?

You’ll need to think through the expense of bring this system back to life.

While I would try replacing the MacBook Pro Unibody 13" and 15" MagSafe DC-In Board if with the MagSafe charger doesn’t respond you my need a new logic board as the GPU chip often fails in this series. While you can bypass it enabling the Intel graphics engine within the CPU. It is not as good as the discrete GPU.

Next given the systems age you will need to replace the battery

All of this can limit its resale value if that is your direction.

Well check out this it might just help you: https://discussions.apple.com/thread/251...

If it is an obscure logic failure, then you most likely won't find it. It would be buried deep in the thousands of little lines on the logic board, impossible to detect with the human eye.

My experience with Macs is that if the GPU fails then it would turn on, but have a distorted or blank display. The GPU failing should not affect the battery light (unless something is REALLY bad and short circuiting something.) An iMac of mine had a failing/failed GPU, and it's display just was looking a little whack for a while before the GPU died completely, and then the only color the GPU would render was pink with ugly white lines all over the screen.

Replace the DC-in board, as that is definitely a thing that could cause this problem. Reseat RAM, and try reseating the connectors that connect the DC board to the logic board.