I'm also having the same kind of problems. I've tried to ping the other pc and that comes back fine, but when I click 'view workgroup computers' after a considerable wait I get an error message saying the network could not be found.
Strangely though I can access the internet through the second networked pc.
As your network seem to work (i.e. you can ping) try this:
Go to network connections
START > CONTROL PANEL > NETWORK CONNECTIONS
Double click the LOCAL ARE NETWORK or whatever you called it
click PROPERTIES
Double click the TCP/IP
Press the ADVANCED button
Go to the WINS tab
select "Enable NetBIOS over TCP/IP"
then click ok, and if asked restart your computer.