Id you are measuring battery voltage on the GROUND side of the device that is not woking that indicates an OPEN ground.
Suggestion Take a test light This is an ice pick like device with a light bulb in the hand and a wire lead with clip. Clip onto the GROUND wire and poke a known good ground spot with the tip.. Do this with a SINGLE LAMP turned on (not the fan though a fan might work) and if you get "Dim" (slow) operation... plus a DIM test lamp. YOU FOUND THE PROBLEM make the ground solid instead of protected (The test lamp is a protected ground. protected against a dead short)
