Wilbur,
Back in the dark ages of the 70's I had a cell tester to test my battery. It measured the specific gravity of each cell and will tell you if you have a bad or weak cell. I have not used one in a long time, but they are cheap and easy to use. The tester comes with a chart and has different colord beads in it and depending on the condition of the battery all some or none of the beads will float. If none float when you fill it you got a dead cell. I speck you can get one at Walmart or a auto store for less than $10.
Good luck
SeaRay
PS
Found this one at Sears for $5.67 Victor Automotive Products Victor Automotive Products V644 Battery Tester - Tools - Mechanics & Auto Tools - Diagnostic Tools & Testers