Ok I was able to see your pictures. This site is messed up on links. It's a Rain Bird valve.
www.sprinklerwarehouse.com/Rain-Bird-100-DV-A-NPT-1-Inch-Angle-Valve-p/100-dv-a-npt.htm
I'm going on the assumption you don't have tools to test the wires.
Try stripping that blue cable back about 3 inches. Cut the green and white wires back below where the end of the blue cable was before you stripped it. Resplice the end of the valve wires also. Reconnect the wires. See if that works.
Can you turn the valve on with the bleeder screw? That the tiny black thing sticking up on top of the valve. When you turn it water will come out. It's supposed to do that. Keep turning it until the valve comes on then leave it like that until you're done running the sprinklers.
Take the green wire off the controller. Cut about a half inch off. Resplice the end and connect it back up to the controller.
You can also try to turn it on by turning the solenoid. That's the thing with the wires coming out of it. Turn it counter clockwise about 1/2 turn. You might find the handle to turn it on another valve. You might be able to do it by hand.