With the battery disconnected are you able to start the system with just plugging in the MagSafe charger? The system should spontaneously boot.
If it does you'll need a new battery [guide|40697]
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=== Update (07/09/2019) ===
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At this point I suspect your logic board has a problem. You’ll need to find someone local to fix it or you could just replace it [guide|38529] has the logic board info inside.
With the battery disconnected are you able to start the system with just plugging in the MagSafe charger? The system should spontaneously boot.
If it does you'll need a new battery [guide|40697]