Water Disp Leaking Kenmore (Whirlpool) Side by side Refrigerator 106.52754100

[MisterEd]

Most of the time the water dispenser leaks (drips).  We keep a cup under it and sometimes overnight it overflows and sometimes it is fine.  It SEEMS like if I pull forward on the dispenser lever the leak will stop. It drips every 10-15 seconds.  Very slow.

Is there some sort of tension device that keeps the lever forward like a spring of some sort? 
Any other obvious thoughts on why this is leaking?

For the life of me I see no way to disassemble the dispenser unit and really prefer not to if it can be avoided (nor do I want to spend money on a service person because the refrig is pretty old at this point.

Attached are pics of the unit.  You can actually see it dripping. No, the foor is not tilted! 

[haroldsappliance]

Replace water valve, part # W10408179

[MisterEd]

Thanks .... is this a "99.9% for sure" cure? 

[haroldsappliance]

Very low water pressure could cause this problem.