Hi, funny story, I've also just purchased an HP 3478A from eBay that doesn't work and am trying to fix it
(post in this topic).
I'm wondering what kind of failure would cause the primary to become an open circuit inside the transformer?
From what you're saying, between 7 and 8 you've got an open circuit (and I assume of course it's an open circuit between 6 and 9, which is what you want)?
One suggestion, but maybe not a smart one given there might be damage inside the transformer, is if you've got a variac, you could try to drive the 100V tap. I'd probably try to remove the whole transformer to test it. I hope I don't have a similar problem as there are a whack of secondary taps (looks like six).
I'm wondering how easy it would be to find a replacement for that transformer; doesn't look hopeful. Personally I'd be loathe to operate anything from a transformer that looks like something bad happened inside. If you're feeling brave you could always tear it apart and try to rewind it ^^'.
I'm going to try and video myself as I try to troubleshoot and repair mine, can't make any promises on how long that would take me to edit and post though.
Good luck!