What you need to do is, jump start the PSU by connecting the green pin to any black pin in the ATX connector. This will power up the Chillcontrol board through the molex. Then all you need to do is short the two pins you connect the case power switch to and that'll start the compressor.
In fact, you could just start your PC with the molex connected to the controller board then short those two pins and that'll start the Vapo.
Jokester