Checking that the dynamo hub works I just bought a second-hand bike for my daughter knowing that the dynamo hub was not working and now I would like to try and repair it.
I tested that the dynamo does not produce electricity.

I also verified that the positive contact wire is always in short-circuit with the hub body, both before and after disassembling the hub.
That to me means there's something seriously wrong inside the dynamo and I will need to replace it, at least the internal magnet.
I am just not 100% sure with these new (to me) hubs.

Can anyone confirm that there should NOT be any contact between the wire and the internal assembly ?

Edit: this is a Shimano DH-3N20 Dynhub. There's only one cable coming out of the assembly. I used a multimeter on the cable and on the shaft. I suspect the previous owner attempted some clumsy repairs, perhaps damaging the cable.
After some pondering, I ended up buying a new hub, hoping to replace the center part without the need to re-build the whole wheel. I share here some information that might be helpful:


even the new Dynamo showed electric contact between the two terminals, so they are NOT isolated from each other and checking that is no proof the dynamo is broken.
opening the new dynamo, without the lever of the wheel to help, has proven challenging even with the proper tools. I had to build a custom one with a plank of wood, drill a hole and nail the dynamo to it. This way I could close the dynamo in a vice and use the plank to apply enough force.
after I successfully replaced the dynamo, I tried to put back together the old one, just to keep spare the parts. As I did that, I rotated the dynamo and felt current on my fingers. I was able to isolate the little wire properly and now I have 2 working dynamos


It is clear, at least to me now, that a dynamo that is short-circuited is very difficult to turn. When the little wire is not making contact the dynamo spins much more easily.