Have you checked the concentration of the acid? When a battery is fully charged, the specific gravity of the acid is going to be 1.265 or so, possibly as much as 1.300. A discharged battery can have a gravity reading as low as 1.100 or less. By measuring the strength of the acid with a hydrometer, you can determine whether or not the battery is accepting a charge. "Sulfated" batteries have the ability to accept a surface charge, but they have little or no reserve capacity. One or two tries at starting will drain them badly. Sometimes a sulfated battery can be reclaimed by repeatedly slow charging it, then running it all the way down by connecting a slow, constant drain like a headlight bulb. Try a few drain/recharge cycles before giving up on this one.
Jerry