Fuse boxes are powered from their connection to the meter, in the garage. "Ground" isn't open to interpretation: it should be in the round hole in a North-American outlet.But the sound of it, you have Romex, wires wrapped in plastic. But I don't like the sound of a fuse box with two fuses in it. Where is that powered from? Modern romex usually has a bare ground wire, but this is old wire. I'm not clear on what you consider to be the ground. If you open a receptacle and look inside, you might be able to see if there is a bare ground wire roll up, which could be connected to the receptacle's ground screw. However, depending on the condition of the wire insulation, if it is brittle, you might be better to leave it alone and instead ask an electrician to make a house call and tell you if you have a electronic cal/fire hazard on your hands.
There's a wire in the receptacle box, and apparently, it features a ground wire in the insulation that has been cut short instead of connected to the box. Very rigid cable and almost no loose cable to pull for tests.
I already asked the FD if it was a fire hazard, but they didn't call back. I guess it's a risk, just not high enough to warrant a CB. Not that I would blindly trust them or the electrician; they can't even agree on the gas stove! For the FD, having a pilot light is forbidden because of the CO and fire hazard, for the gas company it must have one!!