The IP address you see is the one you get. Depending on your service provider, and their options, you could have a Dynamic (changing) IP address or a Static (doesn't change) IP address. Some automatically give you a Static one, others make you pay extra for that.
It has absolutely nothing to do with the laptop's serial number. And, the IP address is there no matter if you connect to the internet or not. You could disconnect all devices from your internet and the address would still exist. It has nothing to do with the device(s), it is the services address.
Also, depending on your setup, if the laptops WiFi is turned on (or Ethernet is connected) then you are on the internet. Even if you aren't in your browser or using a program that accesses the internet.