Suddenly all my scheduled posts 'Missed Schedule'

Running WP 3.5.1 with several plugins, including Jetpack.

As of two days ago, every time I schedule a post in advance, it never posts. It just says ‘Missed Schedule’ on the Posts page, and never appears.

Troubleshooting I have done so far:
1) Disable all plugins. Result: still happens. And when I tried to reenable plugins, Jetpack didn’t work any more, with the error ‘verify_secrets_missing’ and ‘Error Details: The Jetpack server encountered the following client error: Verification took too long’. So now jetpack doesn’t work either.
2) Check to make sure that the cron PHP task is being called. Result: yes, it appears in the log a bajillion times in the last day.
3) Did not try reverting to default theme, since the blog is already hosted on a BARELY modified (cosmetic modifications only) child theme of 2011.
4) Verify that the blog’s address ( https://dogsofsf.com ) resolves properly on the machine, and curl can retrieve it. Result: Yes, it does and yes, it can.
5) Verify that the /etc/hosts file is reasonable. Result: yes, it is.
6) Possibly related: trying to figure out the problem with jetpack, I deleted it, reinstalled it from scratch. Result: same error as above, no change.

The blog is hosted at Hurricane Electric, on Linux, nothing at all interesting about the hosting environment (it’s a relatively recent version of PHP, etc).

Please please please don’t make me learn PHP to troubleshoot it. Last time I started that I could feel my brain cells dying.