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Your router is probably configured to do DHCP and it has a range of IP numbers that it hands out.
On your local network there are essentially two basic things to configure for a particular machine, the netmask (typically 255.255.255.0 for 8-bit local address) and the IP number. With those set statically, you should be able to ping on your local network, provided the machines are physically connected.
You have two commands that may be helpful, ifconfig/ipconfig to inspect the network interface setup on your local machine. You can also use 'arp -a' to list what the machine has seen on the local network, it shows the mapping of ethernet addresses and IP numbers that it happened to see.
In this case I suggest that you step back to a minimal setup and work from there. Connect one machine and try to ping the router, then you can try two machines and see that they can ping each other, then you can set up default route to ping IP numbers on internet. After that you can try ping to a hostname on internet to see that name server lookup works.
Normally you get these settings from the router, but if you prefer static IPs you may need to configure the router accordingly, which may range from easy or tricky (even impossible) depending on the router.
You can also try to connect to your router from a web browser and inspect its setup. This may also display what it sees on the network, what IP number it has handed out and various other things.
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