Bad batteries, replace them.
If you want your new batteries to last as long as possible, charge them as soon as they are discharged and discharge them to no more than 50%. You may have blown a fuse in the converter because of the excessive draw it sees trying to charge a bad battery.
I would say you are #12 with the identical symptoms and issues posted in the Forum, this year. If you wish to know whether the converter is functioning or not, measure across the battery terminals when you have the converter powered. You should see 13.4 VDC or higher.