Here are your parts
Replacement parts for E30EC65E models | AppliancePartsPros.com

Here is the wiring diagram
http://manuals.frigidaire.com/prodinfo_pdf/Lassomption/318046813.pdf

First you have to check that the unit is getting the correct voltage.
L1 to L2 should be 240 volts
L1 to Neutral and L2 to Neutral both have to be 120 volts/
Be very careful as 240 volts is lethal.
If OK
Check that a wire has not burned off in the unit.
If OK
Remove power from the unit and check the transformer primary and secondary windings for continuity. Also check for signs of blown components. I do not have what the resistances should be and am unable to get a service manual for this unit.
Perhaps someone else can add this info.
This would be be very helpful as it may give what the voltages should be that come out of the transformer board.
If the transformer is blown or the board looks blown.
Check each of the control boards for signs of blown components.
I would remove P5 from each of the controls and check the resistances between the pins. They probably should be the same on all boards. Here you are just checking to see if one is different from the others re: it has shorted. You do not want to instal;l a new transformer board and have it blow right away.
Be sure to use your meter in both polarities when doing this re: Pin 1 red lead and pin 2 black lead then measure with pin 1 black lead and pin 2 red lead etc.etc.

Write all this down so you can keep track of it.