The 11.6 voltage at the batteries is way too low. The motors that operate the slides take a lot of current and if any of the connections are not perfect, or the batteries are not fully charged, the slides may not retract. If you hear a click, the switch and the 12 volt fuse is fine. You will have a control box in your basement, where the click is coming from, that actually supplies power to the slides. Check all of the connections on the wires coming to the control box at both ends to make sure that they are secure.
I still think it is a battery problem, just based on the voltage that you are seeing. If you want to double check your batteries, see how much the voltage drops when you push the slide switch. If, after the click, the voltage drops more, than that is a good indication that you have a problem in the battery circuit, not a fuse, etc.