Start Minecraft Server on first Connection

I was wondering if it's possible to have my (Vanilla) Minecraft server not actually start running until someone tries to connect to it? I have full access to the entire server (It's an old computer of mine) and the router/internet. Failing that, how do I make a button on my nginx site to say "start the mc server"? I'm running Ubuntu 14.04

This is possible but you will need a small program listening on the game server's socket and if it receive any data it will then start the server. But the actual game server will need time to start, so the first login attempt on the client will fail as it will time out. When the server has start they will be able to login successfully. I don't know any existing program for that purpose but it wouldn't be that hard to develop.