Here are your parts
Replacement parts for WHIRLPOOL DU810SWPQ3 Undercounter Dishwasher | AppliancePartsPros.com

Here is the tech sheet
http://www.servicematters.com/docs/wiring/Wiring%20Sheet%20-%20W10039930.pdf

I am assuming that the unit not filling is the only problem since you did not mention anything else.
If the unit seems totally dead then a no power or a door switch would be at the top of the list.

Remove the kick plate and check that the overfill switch is being activated.
Could be the unit thinks it is overful due to this switch.
Sometimes the float can get dirty and stick in the up position.

If OK
Measure across the water fill valve when it should be filling.
If it has 120 volts there is a problem with the valve.
1. Could be that the valve is shot.
2. Could be that the filter screen on the input side of the valve is clogged with crud. Remove the valve and check/clead the screen. Do not permanently remove the screen from the valve as it is there to keep crud out of the valve which could hold the valve open and cause a flood.

If it does not have 120 volts.
Check across the overfill switch. If there is 120 across it then the switch is open and probably toast.

If there is not 120 across the overfill switch.
Check the valve and switch combination for 120, if there is no voltage across them then your problem could be a bad wire coming down from the timer or the timer itself.