The horizontal part of the T fitting goes to the inside of the house. This is the main supply for the whole house.

I'm a dummy, I did not think about the hot water faucets in the house. I had the sink, another outside hose bib, bathroom, and flushed two toilets (thinking it was the lowest outlet) open. I left all of those fixtures open while I was vacuuming. It just occurred to me that it might be that lower valve being bad also that's why I can not get the water to stop dripping.

The lower valve looks like it could use replacing.

Where I live, homeowners can put a deposit down on the tools necessary to turn the water off at the street. In a nearby city, you cannot. It depends on who supplies your water.

There are also two shutoffs in the house on both sides of the meter.

If you should decide to replace the shutoff and can turn it off at the street, you would need to cut the verticle pipe. Remove the shutoff by unsoldering at the bottom. Then probably use a repair coupling and two sections of pipe to complete the vertical section.

I have not ventured out in the alley yet where the water meters are. I will have to investigate that if my next try this weekend doesn't pan out. That or just pay someone to do it... one more try, not quite ready to give up yet.

Have you practiced soldering yet?

Replace the shutoff with a 1/4 turn ball valve.

What happens sometimes is that when you don't drain a bit of water off the water heater. It burps back into the cold water system. Turning it to vacation and turning the cold supply off is fine because your working on the cold water system.

Repair couplings allow a copper tube to pass through them whereas a coupling does not.

I soldered electronics before but this is different, I did watch a couple of YouTube videos if that counts :)

Good question though, I will grab me some pipes and cheap fittings to practice on.

Electronics soldering is a start. Soldering with the Tin-Antimony solders can be fun.

The tool with 4 wire brushes, 2 for internal and two for external 1/3 and 3/4 makes life really easy.

Put a piece of pipe vertical. Cut fittings and remove burrs. Test fit.

Clean the inside and outside with the brush to remove the oxides. Apply flux.

Put fitting on top.

Heat fitting not pipe (move torch for uniform heating). Note about when the flux starts to smoke.

Test the temperature with the solder on the OPPOSITE side of the pipe. Once it melts, go around the joint. The solder will suck up by capilary action.

You can have a damp rag handy to wipe the joint for a professional appearance.

After it cools wipe the flux off (baking soda and warm water).

My method of teaching someone to solder.

I did a water heater WITH a friend. I did the tricky joints. He did the others. Then he was able to do a 40 joint job with no issues.

I like to teach defying gravity first because it gives you a better feel.