Hi,

587.15142400
A Frigidaire built Kenmore.

Should it be pumping it out or should it be recurculating the water.
Many ( not all ) do pre-drain first and then advance into the fill mode. Drain, fill, then water circulation.

I have checked to make sure there is water getting to the Water Inlet Valve, and the screen is clean. I got out my trusty volt meter and checked the volts to the Inlet Valve = 9.8 volts AC. I checked the continuity of the float switch good. I checked the volts going to the float switch = 10.2 volts AC. Now it is determined that the float switch is not getting 120 volts. What is the next thing I need to check to see why there is not enough volts getting to the float switch and inlet valve?
Power comes from the timer, through the float switch to the fill valve. Make sure the float is also not mechanically stuck up and not tripping the float switch.

Online diagram that I found