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Ok, you're getting pretty confused here. Need to take some time to understand what you are doing, not just blindly follow instructions, or jump to conclusions.
Let's start with the router, or rather, without the router. Think back to the time when you didn't have one. You connected the computer directly to the modem. The ISP assigned your computer an address via DHCP. You had no choice about that. Their network, their rules.
Now let's put the router back in. Now IT connects to the modem. Now the ISP assigns an IP address TO THE ROUTER, not to your computer anymore. The router's in the place where your computer used to be. It works the same, and does the same, and as far as the ISP can tell, no change took place. Looks the same from their end.
Connect your computer to the router. Now everything is different. Now you are in your own subnet, created by the router, and the rules are whatever you want them to be. For one thing, your router now has a different IP address, and this is its IP from inside the subnet, inside your LAN. Has nothing to do with its IP to the WAN, the internet at large. So it's got two different IP addresses, depending on which side you're on.
Let's say that you browse to whatsmyip.org, and it tells you what your IP address is. That address is the ROUTER's, EXTERNAL IP address. The web site, and the world at large, only see the router. They don't know what's connected to the other side of it, not how many computers there are, or what kind they are. Say you have three computers connected to your router. You use each of them to browse whatsmyip.org. You discover that they all have the same external IP address. How can this be? Because it's the router's IP each time. It takes each request and forwards it out to the internet as if it were its own request. The reply comes back, and is routed to the correct machine. That's what a router does, and why it's called what it is.
Meanwhile, back at the LAN, on this side of the subnet, your router has that different IP, and each of the computers connected to it has a different IP. That's necessary, since no two devices on a single network can have the same IP.
The static IP concern is about the internal LAN IP that your computer has, inside the subnet. That's between you and the router, and doesn't concern the rest of the internet at all.
When you connect to the router, by default it's the router that's assigning your computer an IP addy via DHCP. You're changing that to make it a static address, no longer using DHCP. Say you do that, and again browse to whatsmyip.org, you'll find your address is unchanged. Again, because it's the router's IP on its WAN side. And whether static or dynamic, it will be utterly different from the address you get from ipconfig, because you're talking about two different networks now.
Hope that makes things a little clearer.
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