Oops, guys, you got it. I had it all wrong.
But look at it this way: I asked before I DID it all wrong :-))))
I think now that the tiny posts in the middle are where the current should be applied, and ....that there is no continuity between those posts. Those tiny center posts are what the wires connecting the heater to the pstat and the start button and the light are attached, and they have no continuity between them. For some reason (scary, I know, Todd), I had convinced myself that those brass parts where I attached the copper wire were the terminals, and I do get continuity there, so I hadn't wanted to order a new heater if mine was still working. Now I'm quite positive I was right in the beginning: my heater has failed!!!!
I am ordering parts from Italy today.