Would it be possible to post a pic of what you have? Is it an aftermarket steering wheel or a stocker? It sounds like you do have the horn ring - which would be that metal and plastic ring that holds the cap on. This ring would be held 1/8" to 1/4" above the metal of the steering wheel - usually by a spring that mounts between the end of the steering shaft and the horn button. And the bottom of the wheel, or wheel adapter, should have a copper plate on it that makes contact with what looks like a large BB lodged in the end of a plastic tube. This BB is connected to one of the wires from the horn. Another wire from the horn attaches to that metal and plastic ring you mentioned (at least if I'm picturing what you have correctly). When you press on the horn button a circuit is completed from the wire attached to the metal & plastic ring, through the metal of the wheel itself, then to the copper plate on the bottom of the wheel and then to that giant BB and on down through the wire. If it's a stock steering wheel the connection may be made slightly different - but I think this is basically how most horns work.
However, it sounds like somebody has buggered up the wiring anyhow so who knows what wiring is still connected inside your steering column. Have you pulled the wheel yet to see if there are any unattached wires in the column?
Hope this helps - others might have better understanding of the wiring schematic.