First I went in the basement to see if there was a shut-off in the water line to the sillcock. There was, but someone had stolen the handle to it.
So I turned off the water at the main, down at the bottom of this pipe.
You should be honored to get to see how "special" my basement is, and how up-to-date my pipes are. (Side note--isn't that a great old kitchen table? Someday I'm going to refinish it and bring it back upstairs.)
Getting back to my story: the sillcock continued to drip, even with the main turned off. I did not have a spare handle for the turn-off, and it is not configured for modern handles, anyway. I did not want to take the channellocks to it and mess up the shaft, so replaced the bucket and went to the hardware store to see if I could find a new handle. I wanted to replace the sillcock, too, but couldn't take it off until the shutoff was in place.
The hardware guys at Ace had never seen anything like what my shaft looked like and had no idea how to put a handle on it, because all the modern ones have a square end. They tried to sell me one of those cheapo pot metal ones that has little clamping teeth inside with screws on the outside to engage the teeth with the rod. I have those on my tub and they are crap, so I declined. I bought a kit to fix my kitchen sink faucet, which was also dripping and went to another hardware store, which also is a plumbing store, hoping they had some old stock, because they are, after all, plumbers. I found an old guy and explained my problem. He was sympathetic, but could find nothing to fit my shaft. He suggested I go to the salvage store. I may still do that.
I came back home and fixed the kitchen faucet and put WD 40 on the basement shaft and the nut holding the handle on the sillcock, because I thought I could replace whatever was inside it that wasn't working anymore. I turned on the water and put the bucket back.
Today I turned off the water again and took my channellocks to the shaft. I was running out of options. The WD 40 did it's job and after a while I was able to turn it enough to shut off the water to the sillcock. The nut on the handle of the sillcock also had loosened up enough to remove it--after I spent half an hour looking through my tools for something to remove the nut with. See, my ex bought me a complete cheapo socket set and then lost the most useful size and the tool, so all I have left is a box of unusable sockets. Fortunately I kept his toolbox and raggedy rusty tools, and there was a socket wrench and the right-size socket! --Note to Self--buy a new socket set.--
I got the handle off and the large nut around the shaft and found that the shaft is sealed into the unit and there are no moveable parts to remove. You have to buy a whole new one. This I cannot do because I do not have the tools or the strength to twist the sillcock off the wall. I replaced everything and turned it REALLY HARD and turned the water back on. No dripping. OK, now I have all winter to find a new handle and convince some big burly sort to replace my sillcock.
Bertie is pissed.