I'd start by removing both battery cables and cleaning the end contacts thoroughly. Then after rehooked, check the alternator for output, if you have a voltmeter. It should read anywhere from 13.5 volts to 14.5 volts when running. Unhooking the neg cable will let you know the alternator is putting out, but it won't let you know how much the alternator is putting out. You really need to know exactly what it is producing. So don't discount the alternator just yet. Another possible thing to check would be the battery cables going down underneath, making sure they are whole and connected well, especially if the engine has gotten hot and might've burned a wire somewhere. In my experience when the battery light is lit up on the dash, it is either the battery, the alternator or the wiring. Good luck.