Missing Android asus laptop

I'm not aware of any way you can find it by typing the serial number, I've never heard of such a thing.

If you keep a record of the serial number it just helps to prove that the item belongs to you when it's found by the police or it's handed in to a lost property facility.

The serial number also helps the manufacturer to identify the exact model and it's specifications.
 
The time to prepare for loss or theft is before it happens.

If you had it set up with google+, encrypted it and had one of the security apps like Comoro Mobile Security installed and configured, you'd have a better chance of recovery. You could then sign into one of those apps and have that app lock up the device the next time it connected to the internet.

Better luck next time.