Typically large amp fuses on a converter are 'Reverse Polarity' fuses to protect from battery being connected backwards....cables reversed.
W/O Battery connected ALL of your DC System should have been functioning when pulled into AC Shore Power as converter should have been supplying the DC System
W/O Battery connected converter with 120V AC input should have at minimum 13.2V DC output.....any less and converter is/has failed.
Blowing those fuses........battery cables are backwards OR....if cables have not been removed/re-installed then battery is shorted internally (check specific gravity of each cell)