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There are several fusible links (look like a piece of wire) in the power circuit, one or more of which probably got burnt. You can trace the wires coming out of the battery positive posts and you'll find different color fusible links, such as Gray, Yellow and Blue. If I were in your shoes, I'd start looking for the culprit at the starter relay; they might not look burnt, but they'll give when you tug on them.
Please let me know what you find.