I am sure that you mean physically lost/stolen and just not showing up on a network as expected - correct?
Anyway you cannot search the internet to find the laptop using the serial number (s/n). At best, if the laptop was registered, you might find the laptop's specifications by serial number on the manufacturer's website.
And IP address will not work because when the laptop joins a network it will be dynamically assigned an IP address that will change each time. And if on a private network will not be visible from outside.
If you assigned a static IP then that most likely will have been changed by now so the laptop would work on whatever network it is now a member of.
Unfortunate but there is really nothing that can be done...