Chosen Solution
I have an old MBP which I was going to use for something eventually probably, but to my surprise after spending about a year in a cupboard with a dead batter, it doesn’t switch on anymore. It was fully working when I put it there, and obviously I charged the battery (it’s charging and the indicator is showing full charge), tried with battery and without - when I press power button nothing happens at all.
It does sound like you have a logic board problem. At this point I think you need to bring your system into an independent repair person to get an idea if its repairable. Sadly, Apple will no longer repair this older model. Depending on what they find it may not be worth repairing. Also keep in mind Apple has moved on with newer OS’s which won’t work in this system, the newest you can run is El Capitan OS-X 10.11.x.
