just one correction..
between a private LAN u do not need to specify the gateway and DNS information. it does not help but may render the connection unusable.
Gateway is specified when there needs to be a communication outside ur local network.
DNS is applied when configuring internet access, so that ur pc can resolve urls like google.com and yahoo.com to their IPs to communicate.
In the above configuration the two PCs might not communicate as each will send its data to 192.168.1.1 for further forwarding, as is the work of a gateway, but since there is no 192.168.1.1 no data will reach its destination.
u need to keep he gateway and the DNS blank for a simple two PC communication.