If your blowing that fuse your definitely drawing more than 3 amps, ok we'll assume you dont have a short. Since your battery is completely dead, it'll draw as much as your charger is going to put out assuming its in good operating condition, and if thats 3+ amps your fuse is going to blow. If your charger puts out a max of 5 amps with a completely dead battery, with a 3 amp fuse installed....=blown fuse. Half charged battery, charger might put out half the amps or less 3amp fuse ok.
I think your ok jorge, carry on!