Did the housing (rear case) you purchased include the buttons and its associated flexes or did you transfer everything yourself?
The flexes are very delicate and can tear quite easily. A partially torn flex will not work. Also, when you transfer the buttons, if you don't do it properly, the mechanism can jam or not adequately press the actual actuator (the part that makes electrical contact, sending a "button pushed" signal.
Seeing as how the volume and power button are on the same flex (see below), chances are that is where the problem resides. See this guide for the proper procedure to removing/installing this flex. iPhone 5 Audio Control and Power Button Cable Replacement
So in summary...
- Check the flex to insure it is not torn
- Check the buttons to see if they move freely
- Check the actuators and see if the "click" (they are on the flex, you can see one next to the spudger in this photo)https://d3nevzfk7ii3be.cloudfront.net/ig...
- Check the connector at the end of the flex to see if it is damaged (use a magnifying glass or loupe)
- Check the connector on the logic board to see if it is damaged (use a magnifying glass or loupe)