Hmmm...it does sound like a similar problem but, as it happens, I found the cause of my problem and I doubt that we share it. Nonetheless, I'll try to offer some limited insights.
First of all, for any of those that are interested, my problem turned out to be the Cisco VPN client that I had installed. Even though it WAS NOT operational at the time, it was still blocking traffic somehow. Uninstalling it made everything work.
Now, on to the issue at hand:
The fact your XP machine cannot ping itself, either by name OR by IP address makes me suspicious. Have you tried pinging the loopback address of 127.0.0.1? If that doesn't work, it almost points to a problem in the protocol stack or to some other, obscure XP security setting.
I know you said that you still have SP1 but, if your XP user downloaded an automatic upgrade, then she probably would have gotten SP2 by this point. In that case, the firewall is more complex but you should still be able to configure it. Hmmm...
The DNS problem is not surprising. If the XP machine is not communciating, then it's probably not registering with a DNS server, thus nothing can ping it by name. I have to admit, though, that I am guessing here as I'm not an expert on this stuff but this is how it appeared in my case.
One thing that I found useful was to watch the network connection status on the XP box -- the thing that tells you how many packets were transmitted and how many were received -- and try pinging the box at that time. If the received packed count increments, then you know that packets are being correctly routed to the box.
Another resource for you would be another forum that I've checked into called Annoyances.org. They have a Windows XP discussion forum with some pretty bright folks checking in. You might want to look at that.
That's about all that I can think of. Good luck and let us know what happens.
Cheers,
G