Wont ring. Tighten nuts that hold small bell wires to low-voltage side of transformer. Have someone push the door button. If you hear a hum, the wiring is okay. If you don't, attach short wires to another bell and hold these to the low-voltage terminals of the transformer. Bell should ring if transformer is all right. If it doesn't ring, shut off house current and tighten connections on high-voltage side.
If bell still doesn't ring when power is restored, check whether bell clapper strikes bell. Bend it if it doesn't. Clean contact points inside bell box with emery cloth or fine sandpaper. Bend contact tab on one side of bell to correct vibration speed of clapper rod (some bells have a screw to make this adjustment). If bell still doesn't ring, remove door button and check wire connections. If they appear to be okay, lay a knife blade across the two terminals. If this makes bell ring, clean contact points in button with emery cloth. If bell doesn't ring, however, buy a new button.
If bell still doesn't ring, examine exposed wires running through the house for a break. If you can't see any, attach short wires to a test bell. Then, starting at the transformer, scrape a bit of insulation from the wires at 3' intervals, and touch exposed wires with test bell wires. When test bell stops ringing, you are near break and can easily find it by feel. Then splice broken wires together.