Ah! Think we got a couple of good clues here!
I think we start by replacing your HD SATA cable as you lost access to your drive! Your Hard Drive Cable Is A Ticking Time Bomb
Here’s the needed part MacBook Pro 13" Unibody (Mid 2012) Hard Drive Cable and yes its the 2012 model as that’s the better version of the cable. Here’s the guide you’ll need to follow MacBook Pro 13" Unibody Late 2011 Hard Drive Cable Replacement
Lets see where things are after you replace it.
Well, your system looks quite good given its age! Did you get a chance to read this? Your Hard Drive Cable Is A Ticking Time Bomb I would add in the strip of electricians tape under the cable.
The bends seem to be smooth which is good! Often I see people who crease the cable into a sharp bend which damages the thin foil wires within it.
At this point I think we need to move on to the battery if you can get the system to boot up lets get a snapshot of CoconutBattery take a snapshot of the apps main window and post it here for us to see. It will allow us to see the health of the battery and the charger.