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How was the battery tested?How many miles on the car?
This is a bad connection. This is why the negative cable is getting hot. You should check both ends of the cables, at the battery and at the starter if you are certain that the battery is good. Usually a hot negative cable means there is a poor ground, or the cable itself has some corrosion. Since you can wiggle the cable and get some life back, albeit short,this really indicates a bad connection.
Also, look for any signs of swelling under the insulation on the cable.
Please check this and let me know.