So, my first thought was that the storm might have knocked out our cable service, but then I realized the network cable disconnection message wouldn't support that theory. When the cable has gone out in the past, it didn't give that error. It simply failed to reach addresses on the Internet because that side of the router (WAN) was down, but the local network side (LAN) worked fine.
Since XP had sensed a total disconnection from the LAN, and not just the loss of Internet access, I figured it had to be a problem closer to my computer's actual network cable. My XP machine in my room actually shares a port on the router with my Linux server in the basement. The two are connected to a switch, which in turn is plugged into the router. So I figured a good test would be to ping the Linux server. When that failed, I knew that meant the switch wasn't working. (It could've meant just the server wasn't working, but that wouldn't explain the cable disconnection error message.) I also pinged the router just to be sure, and that failed too.
So I went down to the basement to verify this, and found that both the Linux server and the switch were off. Power failure? But everything else in the house seemed to be working. There weren't any nearby lightning strikes. There were no weird smells to indicate one of the devices shorted or anything. I checked the breaker box and sure enough one of the switches was tripped.
That breaker was the only one in the box of its kind, and looked newer, with a test button and a label with a long number that the others didn't have. I figured it must have been a circuit added when dad semi-finished one side of the basement years ago (from which I had run an extension cord to power the server and switch) and it might also include the outdoor outlets for the xmas lights that I think were added around the same time. I went over to that side of the basement and, sure enough, the lights there didn't work.
I flipped the breaker all the way off then back to on, figuring if the problem still existed it would simply trip again. And a few seconds later, it did just that, so I left it. I'm guessing some rain worked its way into the outdoor outlets. It was coming down pretty hard for a while, and out of the north (into the front of the house).
I ran a temporary extension cord from an outlet on another circuit to power the server and switch for now, and left a note on the kitchen table for dad to see.
Fortunately the server and switch were not harmed when the circuit overloaded. (They don't have a surge protector.)