You got the serial number and maybe could the MAC address be found from serial number?
Then can some service locate that MAC address?
It may have 2 MAC one for LAN and one for wireless.
That ... is actually a really good idea. If you can get the MAC interface address from Apple or somebody, that's built directly into the network hardware of the machine. And on Macbooks, you can't change the network hardware out, because it's built straight onto the motherboard. So if there's a macbook somewhere on the network that's using that MAC interface, then it's the one.
Problem with that is, if it's on the network, that means it's IN USE, presumably has been for three and a half years, and the odds are whatever was on its hard drive has been cleared out to make room for somebody's porno collection.
This is about a one-in-five for finding your macbook, which is better than I'd have ever guessed you could do. But it's still less than one-in-a-thousand for getting your bitcoins back.