What is wrong with my doorbell?

Does the doorbell on have a diode or resistor across the leads? This would be to keep some voltage on the doorbell so it stays alive, like one that has a memory. Ours works like that. Then when you depress the on full voltage is applied to the doorbell. The other possibility is your have a lighted doorbell on. When it isn't depressed, the light is in series with the doorbell which drops the voltage to where the doorbell isn't actuated, but when you depress the on full voltage is applied to the doorbell. It sounds like your doorbell is bad.