Thanks for your question about your refrigerator model 596.76593600, I will be glad to assist you with this concern.
When water flow from the dispenser is reduced, this usually means that either the home water supply is restricted , the inlet valve(water supply connects too) is no longer operative or the filter is clogged and need replacing.
I would suggest you start by testing the water filter. Remove the filter and install your filter bay-pass cap. Now if water flows good again replace the filter to solve the problem. If that did not help you will now need to test the water pressure supplied to the refrigerator by ,unplugging the refrigerator form the power outlet pull the unit away from the wall enough to access behind the unit. Turn off the water supply at the wall then disconnect the water line at the refrigerator. Use a one gallon container, place the loose end of your supply line in the container ans turn the water back on. You should get a strong flow ( about one pint of water in ten seconds) if the flow is not good you will need a plumber to come and test the water lines supplying your outlet to the unit.If the water supply is okay then suspect the water inlet valve that the water supply connects to on the refrigerator(water inlet valve assembly) available through Sears Parts Direct. searspartsdirect.com?sid=MMLxexpertxmerch
I hope this helps. Ron H.