In the mean time..
Until you figure out if you have a converter or if it is fixable you can add another one on, will not hurt things as it is right now since it is obvious that your battery is not getting any charging voltage..
Found a good deal on a deck mounted Iota 30A 12V converter in the electronic surplus stores.. for $39.95!
HERE
These are being sold as used because they are "pulls" from equipment that was not sold and the power cord has been cut and modified (you will need to add a plug).
These converters do not include the IQ-4 smart controller which turn it into a multistage charger. Without the IQ-4 it is set at a fixed 13.6 voltage.
New 30A converters will set you back well over $100..