Did you remove the sump cover and check in the sump?
If not I would do that, check for debris and any thing wrapped around the chopper.
Be careful there is often broken glass in the sump.
Also note how the insert goes in, re-install it wrong and the chopper will eat it.

Checking the water valve for continuity really does not tell you much as it is working so you know that it has continuity.

I believe the unit should fill to just below the heating element.
Often if the fill is low the pump will be noisier because it is sucking in some air.
One way to check the fill, if you feel it is low, is to add a quart or two of hot water after each fill during a cycle.
If the dishes come out clean and/or the pump gets quieter then odds are it is a fill problem.
Just be careful to not overfill it.

If it is a fill problem, shut off the water supply and pull the water valve. There is a screen filter on the input side of the valve. Check./clean the filter.
Do not permanently remove it as it is there to prevent crud from getting into the valve, holding it open and causing a flood.

If the filter is cleran I would replace the water valve.