Our doorbell didn't work when we moved in 6 years ago. Thinking back, I think the reason was the doorbell ringer mechanism was inside the furnace air return, so it got clogged with dust. Instead of trying to fix it, I used the existing from doorbell button to a drive relay which turns on a beeper upstairs. That system is great during the day when I'm in my office, but very much not when we're home, particularly we don't hear it when we're watching TV.
I bought a replacement ringer/bell unit, and as shown below, finally
installed it. First off, I used painters tape to get everything level
and aligned and marked, then drilled a hole into the wall towards the
closet to pass the wires:
Interestingly, someone ran wiring up the middle of the cavity, which
electrical code really discourages you from doing.
There are TWO jacketed feed wires
inside the wall, not connected to the verical posts inside the wall.
I did push the wires aside and drilled through the other side of the
wall, so I can pull wires up through the closet.
Now before installit it I removed all the painter's tape, leaving the
mounting holes and the big hole in the center that will bring the
wires in.
Finally the doorbell chassis installed. Hopefully the wiring will be
finished soon so that both main doors have a doorbell that people can
actually use.
The wiring will take a little time, as I have to join the AC and DC
sides of the doorbell circuits together.