Right. I did read the page at the link you provided.
*I used proper capitalization & a descriptive subject line.
*I was patient! I didn't even reload the board once!
*I made my own topic.
*Hasn't been resolved yet, so...
*I never feel alone when I'm here. <3
*I read the Codex, I do that prior to ANY upgrades, nothing seemed extraordinary.
As I said I did the upgrade first on my test site with all the same plugins running. It worked fine.
The server that won't unpack doesn't give the owner access to "flush caches". In fact, I don't think I've used a server that allows someone hosted on it to flush a cache.
I didn't think there was a need to deactivate all plugins because as I said above, it never finishes unpacking. I'm not sure how active plugins would affect that - and also, it installed on the test server without shutting off all plugins, no problem.
Ironically, this site is using a child theme of 2012. So, yeah, not that.
Maybe I should have said "Any suggestions where to look ON THE SERVER" because I'm thinking that may be where the problem is mainly because Server A = update OK! Server B = update NOT OK!
BTW - I did upgrades on two other sites without problem before coming back here to respond. Not on the same web host, but update went fine, nonetheless.
I could do a manual update, which is fine, but that doesn't answer the question of why won't it go past the unpacking and begs the question is something else broke that I need to address before it causes a huge problem on a very active site. Which I know is NOT the problem of WordPress, but figuring out why there is a problem with the wordpress upgrade could help me to solve the (potential) problem.