Try putting jump leads from the car battery to the bike battery, even new batteries can get a duff cell, which would explain the voltage drop under load. If it works, your "new" battery is duff, if it doesn't, check and double check the earth, especially if the frame has been painted or powder coated, or try a jump lead from the battery negative to a clean engine bolt (no paint on it!) and try it again. What happens if you bridge the 2 terminals on the solenoid with a large screwdriver?
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