If for some reason your Ping returns a timeout message, then you might have another problem. The most common issue has to do with Windows XP and the Internet Connection Firewall (ICF). The Windows XP Network Setup Wizard will sometimes enable ICF on your Ethernet adapter. ICF is designed to protect you from threats outside of your network by blocking unauthorized traffic from reaching your PC. It is supposed to be used only on the interface that directly connects to your Internet connection. However, if ICF is enacted on an interface that is being used to connect to another PC, it will block all the transmissions being sent to it. It will not even respond to pings. ICF must be disabled in order for the connection to work.
To disable ICF simply right-click on "My Network Places" and select Properties. Right-click on your LAN connection and again select Properties. Go to the Advanced tab and uncheck the box that reads "Protect my computer and network by limiting or preventing access to this computer from the Internet." Click OK. Now try to ping the other PC again. It should work fine.