What should I check when troubleshooting a doorbell?

Question

Our doorbell stopped working a while ago and my wife finally bugged me enough to fix it.

First, I found a diagram on another site when I googled this. It is wired like the right box:

I started by measuring the voltage coming out of the transformer which is attached to a junction box in the basement. There is a small amount of power coming out of the transformer, which itself appears to be new relative to everything else in the house. Just to be sure, I turned off the breaker and checked the connections inside the junction box. Same results after.

The doorbell ringer is in the kitchen. When I take off the cover and measure the voltage it matches what I see in the basement. However, when I press either doorbell it does not ring: if I short circuit the screws for a doorbell using a wire, nothing happens: unless I am wrong this should make it ring since it is making a complete circuit and essentially removing the switch/button.

Two other possibly relevant pieces of information. First, one of the doorbell buttons is damaged, it is smashed beyond repair: I have to replace this anyway. Second, my wife swears this all started when my brother (an electrician) replaced the load center a while ago. Since the transformer is 30 feet from the load center and everything else on that circuit works fine, I am doubtful that is the cause. So these are probably red herrings but I have to tell my wife I tried.

My educated guess is that the doorbell unit itself is faulty and needs to be replaced.

My question is this: should I check anything else before spending the money to replace it?

UPDATE: I disconnected the wires from the transformer at the doorbell ringer. I connected it to an AC outlet using one of those adjustable wall-warts. It only goes up to 12V (transformer is 16V) but it rang when I shorted it to one of the switch wires. So I think this is the transformer.

Are these transformers fixable (I do hobby electronics and have rewired rooms in my house)? Or should I buy a new one?

UPDATE 2: I just learned there are two black wires coming out of the transformer, and one of them (does not matter which) needs to be wired to neutral. When this broke, I had replaced the ancient junction box the transformer was attached to with one twice as deep and added conduit to go to an outlet in that under-stairs closet. Everything else worked so I did not think much of it. I am still not sure why one of the wires would not be white since that would make sense, but oh well. I just wired it correctly and it works fine. I will accept BMitch's answer since it is close and helpful.

Also, the erratic results on my multimeter were likely due to both wires being hot. I knew something was not right but should have spent time figuring that out instead of looking elsewhere. Oh well, live and and learn. Thank you all for the feedback.

Answer 1

From the description of odd voltage readings, and the fact that you shorted the connection and still couldn't get the bell to ring, I'm guessing the transformer failed. It wouldn't be the door bell button or that wiring since you eliminated that with the shorting. And since you later tested with another power source and verified that the door bell chimes work, that's also eliminated as a possible failure. The only other thing except for the transformer it could be is the wiring from the transformer to your door bell chimes, but that can be a lot more difficult to repair, depending on how far apart the transformer and chimes are. You can double check the wiring by disconnecting it, shorting one side, and checking the ohm reading with your multi-meter on the other side.

You can pick one up relatively inexpensively from the home improvement store, so I'd start there. Make sure to turn the breaker off before touching anything that's connected to the house wiring, and always test the wires for voltage before touching them. I wouldn't bother with repairing the transformer, they're easy and cheap to replace, but hard to repair.