Yep, electrical wierdness is fairly prevalent. I'm thinking the battery reconnection may solve all but, if not, it should be easy to find the issues.
If you just bought a used rig, there is a good chance that it sat unused for awhile. That is a perfect opportunity for Mr. Oxidation to set up residence in switches and connections. One of the first measurements I'd be taking is if there is power to the range hood switches and the water meter location. If power is present, a flip of the switch should show power on the other side of the switch. If power is present on the device side of the switch, there may be an issue with the device (fan) connection or the device itself. If there is a faulty switch, I try to deoxidize the switch internals with Caig Deoxit spray. That is the last effort before replacing the switch.
Sorry, you may know all about troubleshooting and the above is just blathering. I need to correct for my coffee buzz.
