OK, progress!
If P_CON shows 0V when connected to vcc_gnd via the resistor, it will be OK to just use a wire link for that connection (or an on/off switch).
With that connected, what's the voltage on the 4066_switch pin? You could try connecting that to either ground or a pin that has 5V on it, again via the resistors.
(The resistors reduce the chance of damaging anything while testing connections, by avoiding a direct short that could blow something).
It sounds like there may be two totally separate, floating, 5V supplies, each with its own ground - or I'm misinterpreting some figures...