On more than one occasion, I've been remote to a machine and needed to pull the service tag.  Dell has a mechanism on their site which can get that information for you but I seem to recall it only works when you're physically on the machine and not accessing it through an RDP connection.

Since I access almost every machine while being remote, you can see how that poses a problem.

Necessity is the mother or invention, or at least the mother of investigation which I why I went searching for a solution.

A client attempted to retrieve the service tag on a laptop and was unable to read it from the bottom of the machine.  A quick Google search on my part come up with the following command, when run from a command line, it will spit out the service tag.

wmic bios get serialnumber

For the sake of curiosity, I ran this command on a virtual machine and it spit out a rather long combination of numbers and letters which looks similar to the hex equivalent of a product serial number.