Bill,

You're on the right track,
Yes, you should check the float for free up and down movement , and listen for the water level switch to "click". If that checks good, replace the fill valve,

Part number: AP2921090

Bill,
You'll find it a bit easier to remove the pump assembly and work on it outside the dishwasher.
*** Remove power to the dishwasher ***
1. Remove the front access panel.
2. Disconnect the wiring harness connector from the pump motor.
3. Disconnect the two wires from the operating thermostat mounted on the
pump housing.
4. Diconnect the drain hose from theconnector on the pump by squeezing
the hose clamp with a pair of pliers.
5. Unscrew the tuned sound absorber shaft from the motor housing.
6. turn the four pump mounting supports approximately 90 dgrs.
From inside the cabinet,
7. Remove the lower dishrack and lift the pump and motor assembly from
the unit.
Removing the vertical water tube
1. Remove the upper dish rack.
2. Dislodge the upper portion of the vertical water tube from the plastic
knob on the back of the tube by pressing down on the nozzle.
3. Rotate the lower end of the tube either left or right off the pump
nozzle.
NOTE: Do not pull the vertical water tube forward or up in an attempt to
remove it from the pump nozzle. This will damage the "O" ring seal
in the tube opening.
You'll find it easier to dismantle the pump components, just don't loose any of the interior parts and components.

:) :) :)