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The trigger that caused you to decide to replace the battery and logic board cable certainly can could be the reason why the machine suddenly shuts down after the AC power supply is disconnected.
If there was a liquid spill it would not be out of line to replace a damaged logic board, and a liquid spill could cause the problem you're having. So might a power surge.
Examine the logic board under a magnifier… look closely for burn marks, corrosion or swollen components. If you find some that would indicate a logic board replacement… DIY component replacement requires special tools, solder and lots & lots of practice… it's nothing like soldering a lamp cord.
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