Remove the Button
Pull out button as far as circuit wires allow, then detach wires by loosening terminal screws on button. Bring the two bare wire ends together. If bell rings, you know fault is in button. Install new one by connecting the two wires to terminal screws of new button and reattaching button to your house. Doorbell button is a single-pole switch (two wires attached), and you can place either wire under either screw.