I've started working on replacing the section of pipe that broke.
I'm astounded at how many different, independent problems this section of pipe had.
I think this missing chunk of valve is the result of freezing. It may have been the immediate cause of the water, but it wasn't the only problem.
This is the cold side. When I cut the valve loose, this joint pulled apart completely. (It is pulled apart about 1/4 inch here). When you sweat a copper joint, you need to clean and flux both sections. Done properly, the solder will wick deep into the joint, wet both surfaces, and make a very strong joint. It is surprisingly easy.
Done wrong, you wind up with something like this--you can see bare copper between the ring of blobby, corroded cold solder joint. I'm amazed it held at all.
This is a section of galvanized steel pipe attached to a brass elbow connecting to copper pipe. When connecting copper to galvanized steel, you should use a dielectric joint--basically a section of insulator between the two metals, to prevent galvanic corrosion.
Obviously, brass isn't a proper insulator.
It doesn't really matter which one was the cause--If it didn't go this week, one of the other ones would have let loose soon.