Has anyone done this before?

I'm sure it has been done by lots of people.
I used to do it via TCP socket connections - a server (perl) script on the Windows machine listens on a particular port for the message/ping from the Linux machine.
Upon receipt of the message/ping, the server script then sets in motion the desired process and resumes listening (or whatever).

Chapter 17 of the "Perl Cookbook" is one resource for how to set this up, giving examples of both the "server" side and "client" side code requirements. There are, no doubt, other resources.

Cheers,
Rob