For someone born on a U.S. army base in 1983, in panama, who has lost thier passport, is this where they can get a copy of it?

It probably depends on your specific situation. In 1983 the Canal Zone still existed and was considered US territory. If you lost your US passport, I'd reccomend reaching out to the appropiate US institution. Still, my advise is calling directly and explaining your situation so you can get the correct guidance.

Why aren't the phones answering? 3 weeks ago I called, and after calling several times I was answered by a young lady named Alondra, who agreed to return my call with my request and this is the date that she has not done so. This is how you serve Panamanians living in New York?

Are u asking for a Panama passport or a US passport. If Panama then yes the consulate can help you recover your Panama passport provided you have proof of citizenship. If you are asking about a US passport and you are in the US then thats another story