Locating lost sprinkler heads, valves, piping

Valves should be in a box which has a cover that sits ground level. You should be able to isolate zones in the electronic control box. That way, they're getting full pressure. Run it for 20 minutes, and look for wet spots in the ground. Your heads are there.

As far as plumbing goes...jusy look for the most efficient way to run pipes. That is usually the longest straight runs

What the above poster said. Find the valve box (if there is water flow and you are near the box, you will probably hear and feel when the valve turns on) and turn one valve on at a time. Even though your controller isn’t showing errors, make sure that the valve is actually opening. If not you can always manually turn it on. Make sure you can hear and feel flow through the valve. If it is for the lawn, look for heads/wet spots along the perimeter. That’s where most (but not all) of your heads will be.

Do you have an area that looks like it was more cared for than the rest of the field? A little greener or slightly more even? If so that’s probably your irrigated section.

You need to find your backflow preventer and work downstream from there. Make sure you have water available to the system and then see if you can get the controller to function. If you have to, most irrigation supply companies rent valve finders that can be used to find irrigation valves installed in the landscape. Once you find your valves you can manually turn on valves to determine zones. If the controller won’t turn on the valves you may have a controller issue but more likely a field wiring issue.

Valve finder on Amazon LINK

Follow the wires from the controller. If the controller is on the same side of the house as where your water line runs to the house, chances are your valve box is right next to the controller.

Bent irrigation flag works to find the line. Blows your mind, but it is dead on.

Look through your controller and see if there is a chatter setting.

Only way we ever had luck finding grown over systems other than luck.

First check the back flow and make sure the water is on. Second thing I would do is check the fuse in your clock. If both are ok, you’ve probably got a cut in your multiple cable control wire or a bad short or a disconnect common at the first valve. I would rent a wire tracker at that point and find the first valve in the run and start from there and work out for that point. If the cable is cut you will get a strong signal from the tracker at the break. You may find your problem to the whole system is one of the above. Good luck and I’ll be glad to help if I can...worked golf course irrigation and some residential for years. 25 year superintendent here at your service.
ETA just saw you think you have a big leak...that would be the first fix. Good luck.

The enormity (at least to me) of the situation is that the property is on 3 acres. The previous owner used to use the sprinkler, but probably quit using it about 7 years ago or so. The main water line to the house has three tees on it, that have been shut off and lead to, presumably, three separate areas of the property. The sprinkler controller is on a basement wall opposite side of the house from the said water lines and tees.
I was hoping to resurrect the system, but it may have so many leaks, malfunctioning valves and sprinkler heads now, it may not be worth it.

8. 9 at the most, judging by looking at the wiring coming out of the control box in the basement

I didn't think 8 or 9 zones could cover that much on this 3 acres. I have no idea what amount was set up to be covered originally. The first looks at the property were just a month or so ago, while this summer we got plenty of rain, so all of the grass looked good.
I'm thinking like you, that probably only the immediate area around the house had sprinklers setup. Just not sure how come the whole yard still looks pretty good.