We got our system down to an on and an off button. The same might be done if you can get a spring loaded key switch with two contacts.
If you're using a PC, you can do this. I don't know how to do this on a Mac without voiding the warranty. PC motherboards usually have a header for an external, momentary switch. So, you connect your on switch to that.
That switch triggers the power supply to come on. Most computer power supplies have multiple plugs on the end those should you a +12V DC output.
Connect that +12V DC to a power sequencer from Furman. This will trigger the power outlets to go live when the computer turns on. Plug your audio converters and amps into this.
Connect a MIDI Piston to Hauptwerk's shut down menu item. This will not only shut down the computer but will also trigger the shutdown of the power conditioner.