Those individual machine IP addresses are for identifying the computers to each other and to the server inside your network (called the LAN or Local Area Network). The IP address you need to block in Google Analytics is the one that connects the LAN to the outside internet. Unless your network has an unusual setup, using the browser of any computer or device connecting to the network (including phones using WiFi) to type "what is my IP" into the address bar will return the same IP address for the all the machines inside the network. (Large companies occasionally have multiple outside connections, but it doesn't sound like that's what you're dealing with.)
In addition, most commercial internet connections use static IP addresses so the IP "shouldn't" change, but anytime major changes or outages occur, it's a good idea to doublecheck the IP address to be sure it's stayed the same.
Make sense?
Paul
Sidenote: this is one of the main security purposes of a router. It routes all those internal machines' connections out to the internet through a single IP address, so the nasties out on the internet don't have access to an IP address for an individual machine that they can use to direct attacks against it. Thus the network admin only has to protect one device from direct attack from the nastyweb - the router - instead of having to protect every machine individually.