Wow... A circuit like that would be a piece of cake to wire up.
Trigger a relay from your serial port - no prob. Now, how to turn on the computer...
Oh! I have a remote for my car starter which has a button that turns on the computer. I could run a program on boot up to trigger the serial port! Piece of cake.

(did you catch that?)
Someone come up with a remote that sends an impulse to a receiver and there's your trigger.