I tried ipconfig /flushdns and that didn't help.
As I said before (in an edit, so you may have missed) I tried pinging other domains and they resolved to the same IP on both PCs, and with mwb's information it looks like the domain is resolving to the correct IP/name for Yahoo.
My hosts file is empty (well, every line is commented out) so that shouldn't be the problem.
I set my network adapter to use OpenDNS and now when the websites stop working and I try to ping
www.yahoo.com I get a message saying "Ping requiest could not find host
www.yahoo.com. Please check the name and try again." so when I ping the IP I just get timed out.
That makes me think that when things stop working, I can't even connect to OpenDNS to resolve the IP from the name.
And I'm not panicking. I'm just trying to figure out what it is. If it was a virus at least I'd know and I could take some steps to fix it (even if that meant a format). As it is, I still don't know if it's a software issue or a hardware issue.