Problem solved! It wasn't the relay switch after all, nor was it a faulty turn signal switch. It was the hazard switch on the dashboard! Aparently the circuit runs through this to get to the turning signal - where the buzzing sound was coming from. It wasn't getting the power to do it's job.

I took my car to a nearby mechanic and he did several tests with relay switch, checking all fuses, checking the light bulbs, and finally pulling out the hazard light switch and switching it with a known good one.....voila! hazards work and turn signals work AND no more buzzing!