The cables in your photo aren't power cables; they're the antennas for Airport and Bluetooth. They attach to the card at the lower right of your first photo, and then run through the display clutch hinge into the display assembly. A flat ribbon cable then connects the AP/BT card to the logic board.
MacBook Pro 15" Unibody Mid 2012 AirPort/Bluetooth Board Replacement
MacBook Pro 15" Unibody Mid 2012 AirPort/Bluetooth Cable Replacement
I recently replaced the AP/BT card in my 2012 MacBook Air, because I'd smushed a coax connector on the card. What I discovered is that the wireless still worked, but the range and stability was greatly reduced. It looks to me like the connector on the longer cable in your photo was compressed; had you noticed reduced WiFi/BT functionality before the computer failed? If not, I wouldn't worry about that area.
In many laptop models, the computer won't start up if the battery's completely dead, even if you're connected to a charger. There are a few things you can try:
- Make sure the computer is powered off (check the Caps Lock key to see if it lights up, or check the sleep light on the front edge of the computer; the charger light on the MagSafe connector may not light up if the charger has been damaged). Then plug the computer into AC, and leave it alone for an extended period of time - 24 hours, say. If the charge system is working at all, you may get enough juice into the battery to be able to get the MBP to sound the post chime.
- A quicker way to isolate a battery problem is to open the computer, disconnect the battery from the logic board, then try powering up from AC only. If the chime sounds and the computer boots, then the problem is specific to the battery. The computer is four years old; the battery may be completely worn out by now - replace it.
MacBook Pro 15" Unibody Mid 2012 Battery Replacement
MacBook Pro 15" Unibody (Early 2011 through Mid 2012) Replacement Battery
It's possible the replacement DC-in board was a deadster; where did you get it from? And did you do an SMC reset after you installed the replacement board?