And some continuity checks would also be helpful.
^^ This will tell you if it's the buzzer or something in your car's wiring!
Mine (a '70 Cougar) had a compound issue: the buzzer had an open in the coil right where it is soldered to the main wire. I was able to solder it back together and get good continuity. However, I also found that the PO had cut the wire for the key buzzer at the turn signal switch connector. Luckily I was able to re-pin that wire and insert it into the connector again. Buzzer restored to ...intermittent functionality >.<
My remaining issue turned out to be a gunked up door jamb switch. So it would work in warm weather but not in cold weather ~ even though the courtesy lights all worked fine all the time.
Anyhow, I hope that helps, and I hope you are able to get your buzzer working again!