Here are your parts
Replacement parts for gld4355rfbo models | AppliancePartsPros.com

Here is the tech sheet
http://manuals.frigidaire.com/p.../Kinston/154580201en.pdf

And here is a service manual, your unit should be close to the ones in the manual.
http://frigidaireservicetips.com/pdfs/463_9.pdf

I am assuming the unit is totally dead.
Try getting into the diagnostics.
I would check that you actually have power at the unit with a meter.
Then that both door latch switches are closing.
Then confirm that the control board itself is getting power.

If the above is OK, disconnect the keypad from the control board to see if at least the digital display will fire up.
The problem can be either the control board or the keypad so it becomes a bit of a crap shoot as I cannot find a pin-out diagram for the keypad so that you could check it with a meter.
Hopefully someone else has a better way to troubleshoot this.
I would try the connector cleaning below.
Unplug the unit
Open it up
Remove the ribbon cable from the keypad to the control board at the control board.
Clean the edge connector.
If it is the type where there is not a connector just the insulation is removed, it can be cleaned with a pencil eraser. Do not use an ink eraser as it is too abrasive.
Check the tracks in the ribbon cable for hairline cracks. A magnifying glass helps here.
Would not hurt to clean the connector on the board. Use electronics contact cleaner or isopropyl alcohol and a tooth brush. Be gentle and do not reconnect till all the solvent evaporates.
Reconnect everything and give it a try.