If you can't ping the other IP address, you'll never get it to work...
- Turn off any firewalls on both computers
- Assign/Configure their IP addresses (DHCP, Static, Static DHCP, or Automatic Private IP Addressing)
- Ping each computer from the other, using the IP's you posted above - on computer #1 (with IPA = 192.168.1.1) your command would be
ping 192.168.1.2
; on computer #2 the command would beping 192.168.1.1
If ping doesn't get a reply, then your "network" is not working.