Peter:
Your server (hostname: p-b8efe62f25644) is assigning an address in a different block to your remote computer (hostname: peter2). The easy way to fix it is as follows:
If you are good with command lines, you can issue the following command as administrator on your server to fix your problem (in a DOS window).
Code:
netsh int ip set address "local area connection" static 192.168.1.1 255.255.255.0 192.168.1.1 1
This will assign your server with an IP address of 192.168.1.1, which your remote computer on 192.168.1.3 can access.
If you are not good with command lines, then you will have to get into the network device settings (the same panel that has the "repair" button). Go to the "General" tab and click on "Properties". From there click on "Internet Protocol (TCP/IP)", then click on "Properties". A panel where you can set a static IP address will appear. You should be able to tackle it from there...
BTW: While you will be able to ping back and forth, you may not be able to query the computers by hostname. The simple solution is to setup IP/names in the host file (located under /windows/system32/drivers/etc)
OIC!
P.S. The second way to fix the problem using route tables... would not recommend it since you only have two computers in a LAN.