You must have been thinking of a water pump for the family car. Here's the drain pump for your washer. (At less than half the price you were told). Things to look for would be a kink or other restriction in the drain hose; an obstruction in the pump itself (It's not uncommon to find a coin weighing down on the drain valve [a rubber flap that keeps water from coming back into the pump]).

Also make sure there is some air space around the drain hose in the drain or stand pipe itself. If the hose is stuffed into the drain, or sealed off at the drain, water can siphon back into the machine.

Part number: AP4365341