OK, on both PC's:
1.) Right click My Network Places and select Properties.
2.) Select your network interface (normally Local Area Network Connection). Right click and go to properties.
3.) Click TCP/IP from the list and click the Properties button.
4.) In the IP address field select enter IP manually and type: 192.168.0.1 (192.168.0.2 on the other PC) and Subnet Mask: 255.255.255.0 for both.
You can leave all other fields blank for now.
5.) Now try the ping bit....
BTW, if you do have a firewall disable it for testing purposes at least.