As you do not refer to the 550EX and 430EX in your tests, I assume they are not in use at the time and are not part of the configuration.
Camera sync port to off-camera 580EXII sync port should fire the flash, unless the flash is in Master and Manual mode, in which case the port is disabled.
I would expect problems if a 580EXII is placed on-camera, and also has a pc-sync cable from camera to flash - I know of no benefit in the redundant connection. Have you tried that configuration?
Turning the main flash Off is possible only when in Master Mode. It requires a full E-TTL connection to be in use (hot-shoe, Canon extension cable). If it is off, in what way did "it work"?
As Austin.Manny says, the 580EXII sync port is input only, and only when in the right modes. A cable running from a 580EXII port to say, a 550EX will not fire the 550EX.
There is no optical sync capability in the 580EXII. The Canon command/E-TTL system uses an optical carrier, but is not a simple optical trigger. A PC-sync cable can be used in a "hybrid trigger" configuration under very specific settings.
Perhaps a more useful response could be given if you said precisely what configuration you are trying to achieve.