Dull Chime on doorbell
To ensure there's no problem with the wiring to the button or the button itself, try powering the bell directly. The wiring now should have one transformer wire connected directly to the bell and the other transformer wire going off to the button. Take that second transformer wire and touch it to the second terminal on the bell; the bell should ring.
Not only will this help to rule out the possibility of a problem in half of the circuit, it will also give you an opportunity to see the bell in action and observe whether it might have a problem.