Door locks are unreleated to HVAC lighting. HVAC gets it's lighting from the same circuit that feeds all your other gauges and radio etc. Likely..it's either a broken/loose wire at the hvac head unit or the bulbs burned out.
Door locks, I'd pull the boot at the drivers door open and look for wires that were pinched/bent and broken. This is very common.
Draining.. check your battery cables by removing the bolts, then slide the boots off, if they are green..replace both cables. Have the alt tested right on the car by stopping by your parts store. You'll find out if it's bad fairly quick that way.
