The problem isn't power (at least, not any more); it's that the computer doesn't see an operating system to start from, possibly because it can't see the hard drive. Open the computer up again, and check to be sure that the hard drive is securely connected to the hard drive cable, and the hard drive cable securely connected to the logic board socket.
Remplazo del Disco Duro de un MacBook Unibody Modelo A1342
MacBook Unibody Model A1342 Hard Drive Cable Replacement
If that doesn't work, remove the hard drive and attach it to the computer with a USB interface. Can you boot off the drive that way?
SATA Optical Drive USB Cable
Silicone 2.5" Hard Drive Enclosure with USB 2.0 Cable
If you can boot off the internal drive when it's run externally, then the problem is the interface between the hard drive and the logic board. If the cable connector on the logic board is OK, you can try replacing the hard drive cable.
MacBook Unibody (Model No. A1342) Hard Drive Cable
You can also test bootability with an optical disk (Snow Leopard or later, for your model), or a flash drive with 10.6-10.9 on it. If you boot from an external drive and can see your HD (either in the finder or in Disk Utility), you can try repairing it with Disk Utility.