The problem could be related to your "new" top case power switch or else. To check it out: remove and disconnect the top case from the logic board, find the two power pads on your logic board (see pict), connect the magsafe power adapter to the macbook, briefly bridge the two power pads with a small metallic flat screwdriver and the machine should power on. If you have an external USB keyboard and a mouse you'll be able to work with the machine and check if the issue persist. If you don't get the random shut down then you'll know that the top case is the culprit.
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