If voltage measured at converter and battery are both 4 volts, your converter is not putting out a charging voltage and you are just reading battery voltage at both points of measurement.
Could be just a fuse or possibly no AC input power to converter, but you did state there was 120Vac verified at the converter input. Check fuses if they are readily accessible and remove battery and have it checked, recharge with portable if deemed OK.
If fuses are the cause you can check converter output (carefully) without battery to verify proper operation which is indicated by an output voltage of 13.2 Vdc or higher. If converter has bit the dust, Randy at bestconverter.com should have an easily installed replacement, a positive is that the new converter may have improved charging characteristics, particularly important if you do get new batteries.