I would be suspicious of the battery cables, first, given what you have said. Sometimes they can corrode down inside of the cable, and it doesen't show on the terminal ends. Also, if your ground at the block is dirty, it will sometimes act up the way you describe; loose connections, too - they may not look loose, but on heating and cooling under current draw, they may get just enough increase in resistance to cause more high current draw, thus bringing on the same symptoms as a low or dying battery. In the end, it may well be the battery, but if you want to save some money at the expense of some time, cables are cheaper than a battery, and it costs nothing to go through all of the related connections and clean and tighten them. That's my nickels worth.