I thought removing and then re-installing the driver might help. Actually, I tried both kldload and kldunload and both commands came back with "no such file" yet all the while the Ethernet driver (if_my.ko) was visible right there in /boot/kernel. Furthermore, the /boot/loader.conf file has if_myk_load="YES" so was loading at boot. Ping & traceroute didn't work; however, the other computers on my network worked so it wasn't the router or the ISP's fault. I didn't try eth0 though.

Finally, I reinstalled 6.1 and everything works fine now. Perhaps bringing down and up eth0 would have worked. If this happens again I'll try that. I'm a Unix newb, so all this chaos and frustration is good training.