1. no, it doesn't need to be docked. in fact it shouldn't be docked.
2. when using a multimeter, you need to press the power button while checking the contacts for continuity (or resistance).
3. you say the switch doesn't work anymore. did you short the contacts by over-soldering? or melt the plastic? assuming it's a mini-tactile switch, does it work by pressing the button itself (not the button cover on the docking station)?