Dishwasher will not add water during cycles?

All,
Have 10 year old General Electric - Nautilus model no. GSD3610F00AA Dishwasher.
Dishwasher will sometimes not add water during the wash and rinse cycles.
Turning the cycle switch to rinse and after the water starts back to wash will make it add water.
Can anyone tell me what parts may cause this problem?

Here are your parts
Replacement parts for General Electric GSD3610F00AA Dishwasher | AppliancePartsPros.com

It will be one of 3 parts - timer, float switch or water valve.

I would put the timer at the top of that list.

One way to check it would be to measure the voltage across the valve and float switch when it should be filling and is not. If you have 120 volts then the timer is OK.
Then measure just across the water valve, if you have 120 volts and it does not fill, then the valve needs replacing.
If there is no voltage then it is the float switch. Float may just need cleaning. Note this would be the least likely cause could even be said to be a long shot.

Note: The valve and float switch are wired in series.
The power comes from the timer through the float switch to the valve and then through the valve to the other side of the line.