Unable to upgrade from WordPress 3.9.3 to 4.1

I have not been successful in performing an automatic update (from the Dashboard) of my site from 3.9.3 to 4.1. (It’s strange, but I could swear I already upgraded this site to 4.0 and 4.0.1, but I am not sure how to check that). Anyway, I am running the Firefox browser on a Mac OS 10.10.2, if that matters. I have attempted same with other browsers on same Mac.
Basically, I can select “Please update now” from the dashboard.
This takes me to https://<<my site>>/wp-admin/update-core.php
But, when I click on “Update Now”, basically the process appears to hang.
In the browser status, I can see “Waiting for <my site>…”.
In the browser debugger I can see a single POST call to https://<my site>/wp-admin/update-core.php?action=do-core-upgrade
That’s as far as I get.
Eventually if I stop, I am back in the Admin panel.
If I try to reset, I get the following:
“The connection was reset. The connection to the server was reset while the page was loading.”
Over in my CPanel File Manager (Blue Host), I don’t see any files being touched other than wp-config.php, although the wp-admin/error_log has a DB error on one of my plug-ins (which was deactivated during these attempts). And, it does not seem to matter whether or not the plug-ins or activated or deactivated.I have been successful in adding, deleting, and updating plug-ins on the same site.
I have not tried a manual upgrade to 4.1 because the instructions look a bit intimidating to a newbie.

Any ideas?