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Replacement parts for GE GSD3435F00WW | AppliancePartsPros.com

The solenoid de-energizes but the valve remains in the drain position, even if you try to manually move the cam back to the wash position.
It sounds like the flapper valve has come loose from it's shaft.
Remove the spray arm assy etc., then hold the flapper in the drain position while moving the solenoid cam to see if this is the problem. If you manually force the cam into the wash position then the flapper should also go to wash position but according to the above it does not.

It seems as though the vacuum created by the pump is holding the valve in the drain position.
Actually it is water pressure that holds the flapper shut. When the unit goes into a drain cycle the solenoid is activated for a few seconds. It then deactivates but the water pressure keeps it closed. When the water is pumped out the pressure is reduced and the valve is returned to the wash position by the spring. Seems like this is not happening and the valve is staying closed even with reduced pressure.

If I disconnect power to the pump briefly, or move the door latch to the open position briefly, the valve will return to the wash position.
This seems to go against my earlier logic as stopping the pump/pressure does return the unit to the wash position. Very, very weird!!! Especially when you said that there is no problem with the pump out.

Drain solenoid passes the ohms test, I'm not sure what to check next or what part to replace.
You said earlier that the solenoid does deactivate. I assume that you have monitored it with a meter to see that the voltage to it is shut off after a couple seconds. If it gets power for the full wash cycle then that is the problem but usually this caused the solenoid to overheat and it's plastic components melt.