Routers do this because having a dynamic IP address network requires no configuration on your part.
You can simply plug in your computer and the network will work.
We need to have the correct DNS Server IP addresses not the Default Gateway.
You will not be able to use the Internet if we don't find out what your actual DNS servers are. The first way is to log into your router's web interface and look at your router's status page.
If you want to know more about how networks work check out the information here.
Your router most likely assigns dynamic IP addresses by default.If they ask you why you need them, simply tell them you are trying to setup a static IP address on your computer.If they try to sell you a static external IP address, don't buy it.That same IP address could be handed out to another computer later on.This will prevent both computers from connecting to the Internet.On that page you should see an entry for DNS Servers, or Name Servers. Another way to find out what the correct DNS Servers to use, is to call your local Internet Service Provider or ISP.They should know the IP addresses of your DNS Servers right away.When IP addresses are assigned dynamically, it is the router's job to assign them.Every time a computer reboots it asks the router for an IP address.If two computers end up with the same IP address neither will be able to connect to the Internet.There is a lot of information at the following link.