Not with a serial number, no. The computer doesn't actually ever use it, or know what it is. It's just stamped onto the device to keep a record of manufacturing and sales.
There is software you can install on a computer to trace it in the event that somebody stole it, but I assume you never installed any or you'd be asking how to use that. Another possibility is if you have some kind of remote access set up, you could log into the computer and fire up the webcam to get a look at whoever stole it.
But really, without a lot of hard work, some luck and a healthy dose of computer savvy that you don't seem to have, the best you can do is report it to the police and hope for the best.