Try disconnecting the trackpad flex cable from the main logic board (shown in Step 23 of [guide|135944|this guide]). With the cable and battery disconnected and the bottom plate removed, open the display and set the machine on its side with the MagSafe 2 port facing upward. Then connect the MagSafe charger and press the power button. If it’s able to power on the issue may be due to a failing trackpad flex cable or a failing trackpad. [br]
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If that doesn’t help, you’ll need to do some further troubleshooting with the I/O board and the logic board as the point of failure probably involves one of those two components. Hope this helps!