Check both sides of the trackpad cable, keyboard cable/connector and the back of the trackpad board for corrosion or burnt pins. Try plugging the charger in (with battery disconnected) with the keyboard disconnected first, then the trackpad cable disconnected, then the I/O cable disconnected, to see what is causing the problem. The Macbook should boot when the cable is plugged in, and the battery is disconnected.
If this does not resolve your issue, and the Macbook does not boot with everything but the I/O board disconnected, it will be logic board related. Get a schematic and board view, then measure the power rails. If this is out of your experience level, send it to someone who can do board level repairs.
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