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Replacement parts for General Electric GLD6560L00SS Dishwasher | AppliancePartsPros.com

Can you tell me which part is responsible for asking for water?
It is the control board (Item 905 in Section 1) that asks for the water but there are other parts that can cause your problem.

The overfill (float) switch and the water valve, they are wired in series.

Check that the float switch (Item 308 in Section 2) is being activated (closed)
Sometimes the float (Item 305 in Section 2) can get stuck in the up position. If it is then usually cleaning it will fix the problem.

If the overfill switch is being activated, check for 120 volts across the fill valve (Item 744 in Section 2) when it should be on.

If there is no voltage, check across the fill valve/overfill switch combo.
If there is no voltage there, then the control board is probably toast.
If there is voltage, then check across the overfill switch. If there is voltage across the switch then the switch is shot.

If there is 120 volts across the fill valve then either the fill valve needs replacing or it's filter needs cleaning.
There is a screen filter built into the input side of the valve. Remove the valve from the unit and check/clean the screen filter.
Do not permanently remove the screen filter from the valve as it is there to keep crud out of the valve which could hold it open and cause a flood.