GFCI install in old house
OK first of all you cannot determine whether the box is properly grounded just using a multimeter. The fact that it reads "0V" does not mean it is properly grounded. The only way to determine that would be to confirm that there is a proper ground wire all the way back to the panel, or to confirm that grounded armored cable is used. In your case I would just forget about the ground and disconnect it, you don't need a ground for a GFCI.

Second, try to get the GFCI outlet working without the downstream outlets hooked up to the LOAD side. If you can get the GFCI working by itself but it trips when you hook up the downstream wires, that probably means there is something downstream creating a ground fault and the GFCI is tripping (as it's supposed to). A common cause might be a neutral wire touching a metallic box or a "bootleg ground" where neutral and ground are connected.

If the GFCI doesn't work even on its own, it's probably defective.