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the ground strap is from the tranny to the body.
im talking the starter moter to the tranny it might be a big plate at the back but the point is the same.
electiral flow for starting its pos battery to starter solinod to starter moter into the block from the block to the body, body to neg to battery?
Short answer is YES. The starter to gearbox electrical connection must be good or no start. I have personal experience to prove that. Also be sure the ground cable connections are clean and making good contact.