The "piece" with two lines running through it that you talk about I would assume would be a valve. The valve will have an inlet, from the mainline, and an outlet, to the zone line. If it is leaking bad enough, or there is something stuck inside the valve, it could be causing this issue. First, make sure the actual lines into and out of the valve aren't leaking. You may want to take the valve apart and pull the diaphragm and check to make sure nothing is obstructing the valve. If there are no cracks in the actual plastic valve body itself, that should be ok. You can try replacing the diaphragm itself and see if that fixes your problem.
Tony Posey
Ridge Run Landscapes