No Horn
It sounds like a bad relay.
An easy way to test this theory is to listen cloely when you press the horn button.
If the relay is working, you should hear a faint "click" from under the driver's side dash. The relay is tucked in there and they normally have a blue plastic cover. Relay measures about 1" square.
If there is no faint "click", try removing the relay and reinstalling it. Sometimes corrossion will attack the blade connections, especially if your Vette leaks water under the dash as some do.
If there is a click, then the problem is somewhere between the relay and your horn.