I would start the trouble shooting with first testing the battery, then put a charger on it, 12.7 volts is low, it should be 13.4 or higher. Then I would start testing for 12v power with the battery, then just follow the cables and re test at every connection with a volt meter, or a test light, also make sure your primary ground is good, this should not take that long to find the connection problem, best of luck.
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