When the doorbell doesn't work, I usually can't hear folks knocking at my front door unless I'm on the first floor of the house. Rather than hang up a “Doorbell out of order, wake the dog” sign, most bell problems are pretty easy to diagnose and fix.
The first place I like to check is the transformer to see if there is power to the system. The transformer reduces the 120-volt house current to the 10 or 16 volts AC needed to run the doorbell system. In some old houses it may be a small black box attached to a beam or to a junction box in the basement. It may be attached directly to the electric service panel. I use a multimeter to check for power, if don't you have one, you can use a low-volt circuit tester. If you don't get an indication of power, it's time to replace the transformer.
The most common problem is in the doorbell button or switch. It's exposed to the weather even under a porch roof and the contact points in it will eventually become corroded. A simple enough test, you just unscrew the doorbell button to get to the two wires that are fastened to the back. Touch those two wires together and the bell rings, you'll know the button is bad. If you just get a faint spark without a ring when touching the wires together, it's time to look at the bell.
While the bell unit isn't the cause of most doorbell problems, it can fail on occasion – especially if it is mounted in the kitchen. Dust, tobacco smoke, spider webs and grease can collect in the electromagnetic striker mechanism and gum it up.
Take the cover off the chime unit and have someone try the door button. If the striker moves but doesn't hit the chime, you will have to clean the striker(s).
The chime bar rests on rubber grommets mounted on plastic posts. Gently pull up the bar and pull out the hammer. Spray a light lubrication oil (like WD-40) on a soft cloth and clean the striker. Use a cotton swab to clean out any crud from the electromagnet coil tube. Then wipe off any excess oil which may collect dust.
Put the striker back its place, press it down all the way to its stop, then slip your finger off the top to see if it pops up freely. Replace the chime bar onto the grommets and try the button outside.
If the striker hits the first chime, but the not second chime, pull the striker out again and stretch the spring to give it more tension and replace the striker in the mechanism. Try the button to see if you get a "ding-dong."
Sometimes there's just no fixing the chime unit and you'll have to replace it. Before you disassemble the unit, mark the wires so that you know which one goes to the front door, backdoor and common terminals. Especially important if they are all the same color.
My buddy Russ always reminds me that anything man-made is doomed to failure. Wiring can go bad too, but if this is indeed the problem, it will take some tracking to find where the wire is broken. The wires are a little larger than thick fishing line, and you should be able to see them in your basement ceiling. However, breaks are usually found behind one of the door trim pieces. Locksmiths and door installers can cut the wires with screws or nails when they do their work because the wires are hidden from view.
Once you've found the location of the break, you don't have to replace the whole length of wire – just the part that is broken. Twist the new portion together with the unbroken length and tape with electrical tape.