Here are your parts
Replacement parts for FRIGIDAIRE FDB956RBC1 Frigidaire/dishwasher | AppliancePartsPros.com

Here is your tech sheet
http://manuals.frigidaire.com/prodinfo_pdf/Kinston/154444501.pdf

Remove the kick plate.
Check the over fill switch/float assembly.
Sometimes the float can get stuck in the up position and the unit thinks that it is already full of water.
If it is the float disassemble and clean it.

If switch is being activated.
Measure across the water valve when it should be filling.

If it has 120 volts then either the valve is shot or the filter is clogged.
The valve has a screen filter built into it's input fitting.
You will probably have to remove the valve to check/clean the screen filter.
Do not permanently remove the screen from the valve as it is there to keep crud out of the valve which could hold it open and cause a flood.

If it does not have 120 volts.
Measure across the valve fill switch combo. They are wired in series.
If 120 volts is there odds are that the float switch is toast.
To confirm this, remove power/unplug the unit and check the float switch. It should be 0 ohms.
In no voltage is present odds are that the control board is toast.