You could also buy a hydrometer, that will allow you to test the acid in each cell of the battery. Sometimes batteries I have had on my truck test good on the little machine, and just do not cut it when loaded for a cold start.
I would clean all of the cables as suggested, did you get any of your baking soda bath inside the battery? Also disconnect the GP relay, and see if it will turn over. The GP's could be draining a marginal battery enough to make it not work. It will not start without the GP, but may turn over.

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83 300SD Dark Silver Dark brown inside