It's probably the battery or the logic board. Try the machine with a brand new battery? You can get new batteries for that model pretty cheap online. The instructions for a SMC reset are also extremely specific for that model, so follow the instructions on Apple's website carefully.
I have bought computers online before that turned on a few times, before going belly up as a dead logic board. If it does turn out to be a dead logic board, and if you want to try and resurrect it, there are some last ditch things you can try before throwing it out.
1) Bathe the logic board in Isopropyl Alcohol - then see if it turns on after completely drying out.
2) Cook the logic board in the oven -->read about this online and proceed with extreme caution.
The last ditch things mentioned above sound totally nuts, and they are, but you can read stories and see Youtube videos about people doing crazy 1) and crazy 2) to bring a logic board back to life. I would research, watch videos, and read about this as much as possible before actually trying.
Hope it is just the battery!!!!
It's getting hot in here, so take out your logic board.
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