10 Year old battery????? I would remove the battery take to auto parts store and have it load tested. That thing got to be on it last CELL???? Now that you know the battery is good I would next clean cable ends, no! need to do that anyway using sandpaper polishing both cables and connections at battery, frame, and solinod, also use baking soda if you see any battery acid corrosion that will stop chemical reaction between battery acid and metal parts.

Now that you know you got good battery and connections you can move on to the solonid or starter if you haven't found something and fixed the problem by now????