Quote Originally Posted by inverseparadox View Post
That said, one of my co-workers has reminded me that this may be the model of computer which we've previously seen doesn't get network in ZENboot unless we first go into the UEFI and toggle the network stack between UEFI and whatever the other option is. (It doesn't matter what the old and new values are - what seems to matter is toggling it. Presumably doing so is reinitializing something.)
More specifically, this makes it work until the next boot into Windows, after which things break again until you repeat the toggle.

Quote Originally Posted by inverseparadox View Post
I'm going to test that, and if it gets the network functioning for a single boot, I'm going to try updating the BIOS/UEFI/whatever to its latest release in case that fixes the problem more permanently.
Reporting back just to confirm: yes, the BIOS does appear to have been part of the problem. Updating from BIOS version A02 (what it came with) to A15 (the latest) seems to make things work normally.

The behavior I observed is still a (Linux) bug, given that Windows gets DHCP just fine without this update, but it's an excusable one given that the BIOS version which it happens under is presumably itself buggy.

Sorry to have bothered you; I'm posting this largely in case anyone else encounters the same problem.