I'm having trouble with the "it trys to start but the engine doesnt make a sound" part. Those two statements are mutually exclusive in every scenario I can conjure up. If an engine is not making any sounds how do you know it is trying? More details please

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On the burn't green battery wire: Is this a small green wire that goes into the wiring harness, or the big fat green wire that goes to the engine block or frame?
Did you notice this wire buring while you were trying to crank the starter this time, or is this old damage perhaps from a long time ago?