So this morning, Parallels forgot how to connect to my network. I hadn't changed any settings; it just developed a cold since the last time I ran it. None of the things I found via Google helped, other than by accident; this is what finally did the trick:

• Changed from DHCP to static IP and static DNS/Gateway - still didn't work
• Toggled back to DHCP

After the second step, it worked. Thus the title of the post, with thanks to Troy, who said that in the IRC channel after I described it :)

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