I also have a 63 Galaxie that is doing the exact same thing right now. It ran fine a few days before. Then I went to start it up and got a single click from the solenoid at first. Got a new duralast solenoid, swapped it in, and then got the click again. Went back over all my connections, cleaned them, now I get that buzz when I turn the key. I don't have a voltmeter, but please let me know what ends up happening with your Gal. Similarly, my starter is new and less than a year old. | 
