One of my rear speakers was putting out an awful amount of static when turning the stereo on in my car. I suspected it was coming from the left rear speaker, so I disconnected the wire it and no more static noise.

I plugged the speaker back in and there was no static, but now there's no sound at all (music) coming from the speaker. Does that mean it's pretty much dead and time for a new speaker? It is coming from a car that is 32 years old.

A speaker in a car that is 32 years old could have issues with the paper cone, which over time can get brittle and tear - that may have caused the issue with the static noise. Or perhaps when you disconnected the wires at the speaker the connector broke - again a real possibility with wiring that old. To trouble shoot you can try connecting the speaker wire to a replacement, if you have one available - doesn't matter if it's the correct shape, you just want to confirm that the stereo and wiring are OK.

It is the old paper cone style and it's magnetic. It will magnetically attach to the circular metal port. It actually looked new when I took the speaker cover off. The wire connector attaches to a metal prong on the end of the speaker. They are in-tact. Nothing broke when the speaker was removed. However, I will try another speaker and see what happens.

It could even be a wire connection at the stereo, or anyplace in between the stereo, and speaker. Swap the speakers you have around and see what happens.