Hi there. I'm going to assume that inside that green box is a gate valve that turns the water supply off to your sprinkler system only. This is why you have water to the house and not the sprinklers. I'm always leary about shutting off an old gate valve because they can strip in the off position just as you described. And you can't turn it back on without taking it apart and manually unscrewing it. Or by replacing the valve. I've see a ball valve do the same thing but this is rare. If I'm confusing you with the terms ball and gate valve. They're just two types of shut off valves. If you're confident enough you can unscrew the top half of the valve off and solve the problem. Just remember if you ever have to turn it off again you'll run into the same problem. I suggest replacing the valve. Good luck!
If I can't fix it, it's broken!
