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There are no components between the filter and the dispenser. The flow is controlled by the water inlet solenoid. Most likely it is going out. Replacing the inlet solenoid should resolve the problem.
To locate the solenoid just follow the water line from the source. It connects to the solenoid.
These are a common part and should be available locally from an appliance parts retailer and some home improvement centers (Home Depot, Lowes, and Sears outlets).
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No that is a capacitor. Please do not take that out or try to replace it. Capacitors can carry a very serious amount of stored voltage. If it discharges into you you will not be a happy camper!
Give me a minuet and I will see if I can get you a diagram showing the solenoid.
Ok look at the top left of the back of the unit (facing the back). Is there a cover there? The solenoid should be behind that cover.
Here is a screen shot of the water flow for your unit. If there isnt a cover at the back of the unit then you will have to remove the back of the refrigerator compartment to gain access to the solinoid.
Here are the instructions from the manual.