Not sure what that is in the first picture but it looks like a backflow preventer (assuming). But what is opened in the second picture looks tobe mold growing inside the pipe and probably everywhere else. The second picture looks like a main valve used for city water irrigation. If you can find the first valve or connection from your water source to your irrigation system, cut a section out and turn on the water. It probably is at this backflow preventer. If water flow freely then it is further downstream. PVC pipe is cheap and easy to work with to replace the cutout section. Dig around each sprinkler and unthread the sprinkler to flush the system. If they are pop up then just remove the top part. Rotors must be removed completely as one unit.
If you know the approximate age of this system it maybe easier to replace all valves and sprinklers. If you never dealt with a sprinkler system and have a budget, calling on an irrigation company will be faster. Some homeowners are intimidated by irrigation systems. It can take a lot of digging and working on your knees while bending over.
