Go buy an inexpensive volt meter. Without one you are literally in the dark. Then you can check the voltage at the batteries with the charger on. They should read between 14.1 and 13.5v. If they do, let the charger run for a couple of hours, turn off the charger, let the batteries sit for a while and check them again, if they are fully charged they should read around 12.8v. As they get older that will decrease some. Partially charged (above 50%) somewhere over 12v.
Sounds to me that your batteries are toast. You can take them to NAPA or some other auto supply store and they will check them for you.
If you buy new batteries come back and learn how to check and see if your converter/charger is working correctly or if it is destroying your batteries.
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