I'm sorry - been crazy-busy with about a million things lately. Haven't had the time to post in a while.
Did you try doing a TCP/IP reset on the kid's PC yet?
A couple of potential issues that I see (from your ipconfig output):
1- WINS looks to be disabled. Enabling it on each machine can help with local name-resolution issues. This article
will show how to enable WINS.
2- DNS. Generally, it's preferable for your router to act as a DNS Forwarder (they have this feature for a reason), rather than each workstation doing DNS lookups directly. Your config can, again, create local name-resolution issues.
Try entering your chosen DNS server addresses into your router config, and change the DHCP options on it to point the clients to the router (rather than directly to BellSouth) for DNS lookups.