One thing I could experiment with while my main laptop was busy doing work stuff was the wireless modem. I took the laptop offline, swapped the modems, and fired up the Asus. It found the Internet just fine. So I re-enabled wireless networking on the laptop, and lo, all is well. Conclusion: probably some incompatibility between the AVG firewall and the hardware firewall on the old modem. Normal service has been resumed. Don’t all boo at once.