Usually the buzzer itself dies, can be a broken wire on the ignition switch behind the steering wheel. I had gotten a good buzzer from a cougar hooked it up and it didnt work. I changed my door switch also, nothing... Then 3 years later I dropped my steering column for dash repair and to fix the rag joint. When I pulled the column I noted a small black wire on my ignition switch had snapped off. I decided to replace the switch with a new one.
Put everything back together ,, buzzzzz my ignition key buzzer started working again.